diff --git a/StgSharp.Common/HighPerformance/MatrixKernel.cs b/StgSharp.Common/HighPerformance/MatrixKernel.cs
index 4535487f..1b5adb73 100644
--- a/StgSharp.Common/HighPerformance/MatrixKernel.cs
+++ b/StgSharp.Common/HighPerformance/MatrixKernel.cs
@@ -44,6 +44,8 @@ namespace StgSharp.HighPerformance
     public unsafe struct MatrixKernel<T> where T : unmanaged, INumber<T>
     {
 
+        public static readonly int Size = 16 * sizeof(T);
+
         private T c0r0;
 
         public MatrixKernel()
@@ -58,10 +60,10 @@ namespace StgSharp.HighPerformance
             }
         }
 
-        public ref T this[int column, int row]
+        public ref T this[int row, int column]
         {
             [MethodImpl(MethodImplOptions.AggressiveInlining)]
-            get => ref Unsafe.Add(ref c0r0, (column * 4) + row);
+            get => ref Unsafe.Add(ref c0r0, (row * 4) + column);
         }
 
     }
diff --git a/StgSharp.Common/Mathematics/Linear/CoordinationNaming.md b/StgSharp.Common/Mathematics/Linear/CoordinationNaming.md
new file mode 100644
index 00000000..1f1cc175
--- /dev/null
+++ b/StgSharp.Common/Mathematics/Linear/CoordinationNaming.md
@@ -0,0 +1,88 @@
+# Matrix Coordinate & Naming Conventions (StgSharp)
+
+This document defines the coordinate terminology and naming rules used across `Matrix<T>`, `MatrixKernel<T>`, and packed/triangular storage layouts.  
+Goal: eliminate ambiguity around `column`/`row` names (e.g., “index **of** a column” vs “index **along** a column”).
+
+---
+
+## 1) The key rule: encode prepositions into identifiers (`Of` vs `In`)
+
+### `...OfX` — “which X” (object identity / ordinal)
+Use **`Of`** when the value identifies **which object** (which column, which row, which kernel, etc.).
+
+Examples:
+- `columnOfElement`: the element is located in **which column**
+- `rowOfKernel`: the kernel block is located in **which row**
+
+### `...InX` / `...WithinX` — “inside X” (local coordinate)
+Use **`In`** (or `Within`) when the value is a **local coordinate inside** another object.
+
+Examples:
+- `columnInKernel`: local column coordinate **inside** a kernel block
+- `rowInKernel`: local row coordinate **inside** a kernel block
+
+> Quick mental model: **`Of` = identity**, **`In` = inside**.
+
+---
+
+## 2) Coordinate levels: `Element`, `KernelGrid`, `InKernel`
+
+StgSharp commonly uses three coordinate levels:
+
+1. **Element-level**: final matrix element coordinates (`Matrix<T>[col,row]`)
+2. **Kernel-grid level**: coordinates of a kernel block in the kernel grid
+3. **In-kernel level**: local element coordinates within a kernel (e.g., 4×4)
+
+Recommended names:
+
+| Level | Column name | Row name | Meaning |
+|---|---|---|---|
+| Element | `columnOfElement` | `rowOfElement` | element located in which column/row (0-based) |
+| Kernel grid | `columnOfKernel` | `rowOfKernel` | kernel block located in which kernel-column/kernel-row (0-based) |
+| In-kernel | `columnInKernel` | `rowInKernel` | local coordinate inside the kernel (0..KernelSize-1) |
+
+---
+
+## 3) Index base: 0-based (mandatory)
+
+Unless explicitly documented otherwise, all coordinates are **0-based**:
+
+- `columnOfElement ∈ [0, ColumnLength-1]`
+- `rowOfElement ∈ [0, RowLength-1]`
+- `columnOfKernel ∈ [0, KernelColumnLength-1]`
+- `rowOfKernel ∈ [0, KernelRowLength-1]`
+- `columnInKernel ∈ [0, KernelSize-1]`
+- `rowInKernel ∈ [0, KernelSize-1]`
+
+---
+
+## 4) Mapping element coordinates to kernel coordinates (KernelSize = 4 example)
+
+For a fixed kernel size `KernelSize = 4`:
+
+```csharp
+int columnOfKernel = columnOfElement / 4;
+int rowOfKernel    = rowOfElement    / 4;
+
+int columnInKernel = columnOfElement % 4;
+int rowInKernel    = rowOfElement    % 4;
+```
+
+If `columnOfElement` and `rowOfElement` are guaranteed non-negative, bit operations can be used:
+
+```csharp
+int columnOfKernel = columnOfElement >> 2;
+int rowOfKernel    = rowOfElement    >> 2;
+
+int columnInKernel = columnOfElement & 3;
+int rowInKernel    = rowOfElement    & 3;
+```
+
+---
+
+## 5) Packed storage: distinguish `Index` from `Offset`
+
+Packed layouts do **not** store “empty blocks”; stored blocks are placed contiguously in a packed buffer.
+
+### Use the correct terms
+- **`packedKernelIndex`**: “the N-th kernel
diff --git a/StgSharp.Common/Mathematics/Linear/Matrix.Create.cs b/StgSharp.Common/Mathematics/Linear/Matrix.Create.cs
new file mode 100644
index 00000000..507672d5
--- /dev/null
+++ b/StgSharp.Common/Mathematics/Linear/Matrix.Create.cs
@@ -0,0 +1,104 @@
+//-----------------------------------------------------------------------
+// -----------------------------------------------------------------------
+// file="Matrix.Create"
+// Project: StgSharp
+// AuthorGroup: Nitload
+// Copyright (c) Nitload. All rights reserved.
+//     
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+//
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+//     
+// -----------------------------------------------------------------------
+// -----------------------------------------------------------------------
+using StgSharp.HighPerformance;
+using StgSharp.HighPerformance.Memory;
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Runtime.CompilerServices;
+using System.Text;
+using System.Threading.Tasks;
+
+namespace StgSharp.Mathematics.Numeric
+{
+    public unsafe partial class Matrix<T>
+    {
+
+        private const int KernelSideLength = 4;
+
+        public static Matrix<T> Create(
+                                int columnLength,
+                                int rowLength,
+                                MatrixLayout layout,
+                                HybridLayerSegregatedFitAllocator allocator)
+        {
+            ArgumentNullException.ThrowIfNull(allocator);
+
+            ArgumentOutOfRangeException.ThrowIfNegativeOrZero(columnLength);
+
+            ArgumentOutOfRangeException.ThrowIfNegativeOrZero(rowLength);
+
+            int kernelColumns = DivideRoundUp(columnLength, KernelSideLength);
+            int kernelRows = DivideRoundUp(rowLength, KernelSideLength);
+
+            if (layout is MatrixLayout.UpperTriangle or MatrixLayout.LowerTriangle)
+            {
+                if (kernelColumns != kernelRows) {
+                    throw new ArgumentException("Triangular layouts require square matrices.");
+                }
+            }
+
+            long kernelCount = layout switch
+            {
+                MatrixLayout.DenseRectangle => (long)kernelColumns * kernelRows,
+                MatrixLayout.UpperTriangle => TriangularKernelCount(kernelColumns),
+                MatrixLayout.LowerTriangle => TriangularKernelCount(kernelRows),
+                _ => throw new ArgumentOutOfRangeException(nameof(layout))
+            };
+
+            long requiredBytes = kernelCount * MatrixKernel<T>.Size;
+            if (requiredBytes <= 0 || requiredBytes > uint.MaxValue) {
+                throw new ArgumentOutOfRangeException(nameof(requiredBytes), "Requested matrix exceeds allocator capacity.");
+            }
+
+            HybridLayerSegregatedFitAllocationHandle handle = allocator.Alloc((uint)requiredBytes);
+            MatrixStorageHLSF<T> storage = new MatrixStorageHLSF<T>(allocator, handle);
+
+            Matrix<T> matrix = new Matrix<T>(MatrixKernelBoarder.Create(layout), new MatrixSize(columnLength,
+                                                                                                rowLength,
+                                                                                                kernelColumns,
+                                                                                                kernelRows), storage);
+
+            return matrix;
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        private static int DivideRoundUp(int value, int divisor)
+        {
+            return (value + (divisor - 1)) / divisor;
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        private static long TriangularKernelCount(int order)
+        {
+            long n = order;
+            return (n * (n + 1L)) / 2L;
+        }
+
+    }
+}
diff --git a/StgSharp.Common/Mathematics/Linear/Matrix.cs b/StgSharp.Common/Mathematics/Linear/Matrix.cs
index 5738ecca..26bfd118 100644
--- a/StgSharp.Common/Mathematics/Linear/Matrix.cs
+++ b/StgSharp.Common/Mathematics/Linear/Matrix.cs
@@ -25,59 +25,140 @@
 //     
 // -----------------------------------------------------------------------
 // -----------------------------------------------------------------------
+using StgSharp.HighPerformance;
+using StgSharp.Mathematics.Numeric;
 using System;
-using System.Collections.Generic;
-using System.Linq;
 using System.Numerics;
 using System.Runtime.CompilerServices;
-using System.Text;
-using System.Threading.Tasks;
 
-using hlsfAllocator = global::StgSharp.HighPerformance.Memory.HybridLayerSegregatedFitAllocator;
+// using hlsfHandle = global::StgSharp.HighPerformance.Memory.HybridLayerSegregatedFitAllocationHandle;
 
 namespace StgSharp.Mathematics.Numeric
 {
-    public static class Matrix
+    public unsafe partial class Matrix<T> where T : unmanaged, INumber<T>
     {
 
-        public static hlsfAllocator? DefaultAllocator
+        private protected static readonly int t_count = 16 / sizeof(T);
+
+        private protected static readonly int t_size = sizeof(T);
+        private readonly MatrixKernelBoarder _boarder;
+        private readonly MatrixSize _size;
+        private readonly MatrixStorage<T> _buffer;
+
+        private protected Matrix(
+                          MatrixKernelBoarder boarder,
+                          MatrixSize size,
+                          MatrixStorage<T> buffer
+
+            )
+        {
+            _boarder = boarder;
+            _size = size;
+            _buffer = buffer;
+        }
+
+        public T this[int x, int y]
         {
             get
             {
-                ArgumentNullException.ThrowIfNull(field, nameof(DefaultAllocator));
-                return null;
+                if (y < 0 || y > _size.ElementColumnLength || x < 0 || x > _size.ElementRowLength) {
+                    throw new ArgumentOutOfRangeException($"Index [{x},{y}] is out of matrix index range.");
+                }
+
+                int
+                    k_c = y / 4,
+                    k_r = x / 4,
+                    c = y % 4,
+                    r = x % 4;
+                ref MatrixKernel<T> kernel = ref GetMatrixKernel(k_c, k_r);
+                return Unsafe.IsNullRef(ref kernel) ? T.Zero : kernel[c, r];
             }
-            set;
-        } = null;
-
-        public static MatrixAllocation DefaultAllocation { get; set; } = MatrixAllocation.GC;
-
-        public static Matrix<T> FromDefault<T>(int columnLength, int rowLength)
-            where T : unmanaged, INumber<T>
-        {
-            return DefaultAllocation switch
+            set
             {
-                MatrixAllocation.GC => FromGC<T>(columnLength, rowLength),
-                MatrixAllocation.HLSF => FromHlsf<T>(columnLength, rowLength, DefaultAllocator!),
-                _ => throw new NotSupportedException("This allocation is not supported."),
-            };
+                if (y < 0 || y > _size.ElementColumnLength || x < 0 || x > _size.ElementRowLength) {
+                    throw new ArgumentOutOfRangeException($"Index [{x},{y}] is out of matrix index range.");
+                }
+
+                int
+                    k_c = y / 4,
+                    k_r = x / 4,
+                    c = y % 4,
+                    r = x % 4;
+                ref MatrixKernel<T> kernel = ref GetMatrixKernel(k_c, k_r);
+                if (!Unsafe.IsNullRef(ref kernel)) {
+                    kernel[c, r] = value;
+                }
+            }
         }
 
-        public static Matrix<T> FromGC<T>(int columnLength, int rowLength)
-            where T : unmanaged, INumber<T>
+        /// <summary>
+        ///   Matlab style indexer to generate a new matrix
+        /// </summary>
+        /// <param name="column">
+        ///
+        /// </param>
+        /// <param name="row">
+        ///
+        /// </param>
+        /// <returns>
+        ///
+        /// </returns>
+        /// <exception cref="NotImplementedException">
+        ///
+        /// </exception>
+        public unsafe Matrix<T> this[
+                                ReadOnlySpan<MatrixIndex> column,
+                                ReadOnlySpan<MatrixIndex> row]
         {
-            return new GCMatrix<T>(columnLength, rowLength);
+            get { throw new NotImplementedException(); }
+            set { throw new NotImplementedException(); }
+        }
+
+        /// <summary>
+        ///   Length of the matrix in columns.
+        /// </summary>
+        public int ColumnLength => _size.ElementColumnLength;
+
+        /// <summary>
+        ///   Length of the matrix in rows.
+        /// </summary>
+        public int RowLength => _size.ElementRowLength;
+
+        public MatrixLayout Layout { get; init; }
+
+        internal MatrixKernel<T>* Buffer
+        {
+            [MethodImpl(MethodImplOptions.AggressiveInlining)]
+            get => (MatrixKernel<T>*)_buffer.BufferPointer;
+        }
+
+        protected internal int KernelColumnLength => _size.KernelColumnLength;
+
+        protected internal int KernelRowLength => _size.KernelRowLength;
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public unsafe ref MatrixKernel<T> GetMatrixKernel(int x, int y)
+        {
+            MatrixKernelEnumerator enumerator = new(_size.KernelColumnLength, _size.KernelRowLength,
+                                                    x, y);
+            return ref _boarder.IsInBuffer(x, y, in enumerator) ?
+                       ref _buffer[_boarder.GetIndexOffset(x, y, in enumerator)] :
+                       ref Unsafe.NullRef<MatrixKernel<T>>();
         }
 
         [MethodImpl(MethodImplOptions.AggressiveInlining)]
-        public static Matrix<T> FromHlsf<T>(
-                                int columnLength,
-                                int rowLength,
-                                hlsfAllocator allocator)
-            where T : unmanaged, INumber<T>
+        internal unsafe ref T GetElementUnsafe(int x, int y)
         {
-            ArgumentNullException.ThrowIfNull(allocator, nameof(allocator));
-            return new HlsfMatrix<T>(columnLength, rowLength, allocator);
+            // Caller guarantees: indices in range, layout is dense square.
+            int k_c = y >> 2;
+            int k_r = x >> 2;
+            int c = y & 3;
+            int r = x & 3;
+
+            MatrixKernelEnumerator enumerator = new(_size.KernelColumnLength, _size.KernelRowLength,
+                                                    k_c, k_r);
+            ref MatrixKernel<T> kernel = ref _buffer[_boarder.GetIndexOffset(k_c, k_r, in enumerator)];
+            return ref kernel[c, r];
         }
 
     }
diff --git a/StgSharp.Common/Mathematics/Linear/MatrixMetadata.cs b/StgSharp.Common/Mathematics/Linear/MatrixMetadata.cs
new file mode 100644
index 00000000..253710cd
--- /dev/null
+++ b/StgSharp.Common/Mathematics/Linear/MatrixMetadata.cs
@@ -0,0 +1,234 @@
+//-----------------------------------------------------------------------
+// -----------------------------------------------------------------------
+// file="MatrixMetadata"
+// Project: StgSharp
+// AuthorGroup: Nitload
+// Copyright (c) Nitload. All rights reserved.
+//     
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+//
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+//     
+// -----------------------------------------------------------------------
+// -----------------------------------------------------------------------
+using System;
+using System.Runtime.CompilerServices;
+using System.Runtime.InteropServices;
+
+namespace StgSharp.Mathematics.Numeric
+{
+    public enum MatrixLayout
+    {
+
+        DenseRectangle,
+        UpperTriangle,
+        LowerTriangle,
+
+    }
+
+    public abstract class MatrixKernelBoarder
+    {
+
+        private static readonly MatrixKernelBoarder DenseSquareInstance = new DenseSquareKernelBoarder();
+        private static readonly MatrixKernelBoarder LowerTriangleInstance = new LowerTriangleKernelBoarder();
+        private static readonly MatrixKernelBoarder UpperTriangleInstance = new UpperTriangleKernelBoarder();
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public static MatrixKernelBoarder Create(MatrixLayout layout)
+        {
+            return layout switch
+            {
+                MatrixLayout.DenseRectangle => DenseSquareInstance,
+                MatrixLayout.UpperTriangle => UpperTriangleInstance,
+                MatrixLayout.LowerTriangle => LowerTriangleInstance,
+                _ => throw new ArgumentOutOfRangeException(nameof(layout)),
+            };
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public abstract long GetIndexOffset(
+                             int xKernel,
+                             int yKernel,
+                             in MatrixKernelEnumerator enumerator);
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public abstract bool IsInBuffer(
+                             int xKernel,
+                             int yKernel,
+                             in MatrixKernelEnumerator enumerator);
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        protected static long GetTriangularOrder(in MatrixKernelEnumerator enumerator)
+        {
+            return Math.Min(enumerator.KernelColumnLength, enumerator.KernelRowLength);
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        protected static bool IsWithinKernelDomain(
+                              in MatrixKernelEnumerator enumerator,
+                              int xKernel,
+                              int yKernel)
+        {
+            return xKernel >= 0 &&
+                   yKernel >= 0 &&
+                   xKernel < enumerator.KernelColumnLength &&
+                   yKernel < enumerator.KernelRowLength;
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        protected static bool IsWithinTriangularDomain(
+                              in MatrixKernelEnumerator enumerator,
+                              int xKernel,
+                              int yKernel)
+        {
+            long order = GetTriangularOrder(enumerator);
+            return xKernel >= 0 && yKernel >= 0 && xKernel < order && yKernel < order;
+        }
+
+        private sealed class DenseSquareKernelBoarder : MatrixKernelBoarder
+        {
+
+            [MethodImpl(MethodImplOptions.AggressiveInlining)]
+            public override long GetIndexOffset(
+                                 int xKernel,
+                                 int yKernel,
+                                 in MatrixKernelEnumerator enumerator)
+            {
+                long x = xKernel;
+                long y = yKernel;
+                long rows = enumerator.KernelRowLength;
+                return x * rows + y;
+            }
+
+            [MethodImpl(MethodImplOptions.AggressiveInlining)]
+            public override bool IsInBuffer(
+                                 int xKernel,
+                                 int yKernel,
+                                 in MatrixKernelEnumerator enumerator)
+            {
+                return IsWithinKernelDomain(enumerator, xKernel, yKernel);
+            }
+
+        }
+
+        private sealed class LowerTriangleKernelBoarder : MatrixKernelBoarder
+        {
+
+            [MethodImpl(MethodImplOptions.AggressiveInlining)]
+            public override long GetIndexOffset(
+                                 int xKernel,
+                                 int yKernel,
+                                 in MatrixKernelEnumerator enumerator)
+            {
+                long order = GetTriangularOrder(enumerator);
+                long x = xKernel;
+                long y = yKernel;
+
+                long prefixColumns = x * order - (x * (x - 1L)) / 2L;
+                return prefixColumns + (y - x);
+            }
+
+            [MethodImpl(MethodImplOptions.AggressiveInlining)]
+            public override bool IsInBuffer(
+                                 int xKernel,
+                                 int yKernel,
+                                 in MatrixKernelEnumerator enumerator)
+            {
+                return IsWithinTriangularDomain(enumerator, xKernel, yKernel) && yKernel >= xKernel;
+            }
+
+        }
+
+        private sealed unsafe class UpperTriangleKernelBoarder : MatrixKernelBoarder
+        {
+
+            [MethodImpl(MethodImplOptions.AggressiveInlining)]
+            public override long GetIndexOffset(
+                                 int xKernel,
+                                 int yKernel,
+                                 in MatrixKernelEnumerator enumerator)
+            {
+                long x = xKernel;
+                long y = yKernel;
+
+                long prefixColumns = (x * (x + 1L)) / 2L;
+                return prefixColumns + y;
+            }
+
+            [MethodImpl(MethodImplOptions.AggressiveInlining)]
+            public override bool IsInBuffer(
+                                 int xKernel,
+                                 int yKernel,
+                                 in MatrixKernelEnumerator enumerator)
+            {
+                return IsWithinTriangularDomain(enumerator, xKernel, yKernel) && yKernel <= xKernel;
+            }
+
+        }
+
+    }
+
+    [StructLayout(LayoutKind.Explicit)]
+    public struct MatrixSize
+    {
+
+        [FieldOffset(0)] public readonly int ElementColumnLength;
+        [FieldOffset(4)] public readonly int ElementRowLength;
+
+        [FieldOffset(8)] public readonly int KernelColumnLength;
+        [FieldOffset(12)] public readonly int KernelRowLength;
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public MatrixSize(
+               int elementColumnLength,
+               int elementRowLength,
+               int kernelColumnLength,
+               int kernelRowLength)
+        {
+            ElementColumnLength = elementColumnLength;
+            ElementRowLength = elementRowLength;
+            KernelColumnLength = kernelColumnLength;
+            KernelRowLength = kernelRowLength;
+        }
+
+    }
+
+    [StructLayout(LayoutKind.Explicit)]
+    public struct MatrixKernelEnumerator
+    {
+
+        [FieldOffset(0)] public int CurrentColumn;
+        [FieldOffset(4)] public int CurrentRow;
+
+        [FieldOffset(8)] public readonly int KernelColumnLength;
+        [FieldOffset(12)] public readonly int KernelRowLength;
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public MatrixKernelEnumerator(
+               int kernelColumnLength,
+               int kernelRowLength,
+               int currentColumn = 0,
+               int currentRow = 0)
+        {
+            CurrentColumn = currentColumn;
+            CurrentRow = currentRow;
+            KernelColumnLength = kernelColumnLength;
+            KernelRowLength = kernelRowLength;
+        }
+
+    }
+}
diff --git a/StgSharp.Common/Mathematics/Linear/MatrixEnum.cs b/StgSharp.Common/Mathematics/Linear/MatrixStorage.cs
similarity index 55%
rename from StgSharp.Common/Mathematics/Linear/MatrixEnum.cs
rename to StgSharp.Common/Mathematics/Linear/MatrixStorage.cs
index 4c0aee51..6df883fd 100644
--- a/StgSharp.Common/Mathematics/Linear/MatrixEnum.cs
+++ b/StgSharp.Common/Mathematics/Linear/MatrixStorage.cs
@@ -1,6 +1,6 @@
-//-----------------------------------------------------------------------
+//-----------------------------------------------------------------------
 // -----------------------------------------------------------------------
-// file="MatrixEnum"
+// file="MatrixStorage"
 // Project: StgSharp
 // AuthorGroup: Nitload
 // Copyright (c) Nitload. All rights reserved.
@@ -25,19 +25,48 @@
 //     
 // -----------------------------------------------------------------------
 // -----------------------------------------------------------------------
+using StgSharp.HighPerformance;
+using StgSharp.HighPerformance.Memory;
 using System;
 using System.Collections.Generic;
 using System.Linq;
+using System.Numerics;
+using System.Runtime.CompilerServices;
 using System.Text;
 using System.Threading.Tasks;
 
+using HLSFAllocator = global::StgSharp.HighPerformance.Memory.HybridLayerSegregatedFitAllocator;
+using HLSFHandle = global::StgSharp.HighPerformance.Memory.HybridLayerSegregatedFitAllocationHandle;
+
 namespace StgSharp.Mathematics.Numeric
 {
-    public enum MatrixAllocation
+    public abstract class MatrixStorage<T> : IDisposable where T : unmanaged, INumber<T>
     {
 
-        HLSF,
-        GC,
+        internal unsafe ref MatrixKernel<T> this[long index]
+        {
+            get { return ref Unsafe.AsRef<MatrixKernel<T>>(BufferPointer + MatrixKernel<T>.Size * index); }
+        }
+
+        protected internal abstract unsafe T* BufferPointer { get; }
+
+        public abstract void Dispose();
+
+    }
+
+    internal class MatrixStorageHLSF<T>(HLSFAllocator allocator, HLSFHandle handle) : MatrixStorage<T>
+        where T : unmanaged, INumber<T>
+    {
+
+        internal HLSFAllocator _allocator = allocator;
+        internal HLSFHandle _handle = handle;
+
+        protected internal override unsafe T* BufferPointer => (T*)_handle.Pointer;
+
+        public override void Dispose()
+        {
+            allocator.Free(_handle);
+        }
 
     }
 }
diff --git a/StgSharp.Common/Mathematics/Linear/Matrix_T.GC.cs b/StgSharp.Common/Mathematics/Linear/Matrix_T.GC.cs
deleted file mode 100644
index 5d971427..00000000
--- a/StgSharp.Common/Mathematics/Linear/Matrix_T.GC.cs
+++ /dev/null
@@ -1,124 +0,0 @@
-//-----------------------------------------------------------------------
-// -----------------------------------------------------------------------
-// file="Matrix_T.GC"
-// Project: StgSharp
-// AuthorGroup: Nitload
-// Copyright (c) Nitload. All rights reserved.
-//     
-// Permission is hereby granted, free of charge, to any person obtaining a copy
-// of this software and associated documentation files (the "Software"), to deal
-// in the Software without restriction, including without limitation the rights
-// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
-// copies of the Software, and to permit persons to whom the Software is
-// furnished to do so, subject to the following conditions:
-//
-// The above copyright notice and this permission notice shall be included in all
-// copies or substantial portions of the Software.
-//
-// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
-// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
-// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
-// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
-// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
-// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
-// SOFTWARE.
-//     
-// -----------------------------------------------------------------------
-// -----------------------------------------------------------------------
-using StgSharp.HighPerformance;
-using StgSharp.Mathematics;
-using System;
-using System.Collections.Generic;
-using System.Linq;
-using System.Numerics;
-using System.Runtime.CompilerServices;
-using System.Runtime.InteropServices;
-using System.Text;
-using System.Threading.Tasks;
-
-namespace StgSharp.Mathematics.Numeric
-{
-    internal unsafe partial class GCMatrix<T> : Matrix<T> where T : unmanaged, INumber<T>
-    {
-
-        private readonly MatrixKernel<T>* _buffer;
-
-        public GCMatrix(int column, int row)
-        {
-            KernelColumnLength = (column + 3) / 4;
-            KernelRowLength = (row + 3) / t_count;
-            ColumnLength = column;
-            RowLength = row;
-            _buffer = (MatrixKernel<T>*)NativeMemory.AlignedAlloc((nuint)(column * row * sizeof(T)), (nuint)World.DefaultSIMDAlignment);
-        }
-
-        public override ref T this[int column, int row]
-        {
-            get
-            {
-                AssertIndex(column, row);
-                int kernelColumn = column / 4, c = column % 4;
-                int kernelRow = row / t_count, r = row % t_count;
-                ref MatrixKernel<T> kernel = ref _buffer[kernelColumn + KernelColumnLength * kernelRow];
-                return ref kernel[c, r];
-            }
-        }
-
-        public override Matrix<T> this[ReadOnlySpan<MatrixIndex> column, ReadOnlySpan<MatrixIndex> row]
-        {
-            get => throw new NotImplementedException();
-            set => throw new NotImplementedException();
-        }
-
-        internal override unsafe MatrixKernel<T>* Buffer
-        {
-            [MethodImpl(MethodImplOptions.AggressiveInlining)]
-            get => _buffer;
-        }
-
-        public override unsafe ref MatrixKernel<T> GetMatrixKernel(int column, int row)
-        {
-            AssertIndex(column, row);
-            int kernelColumn = column / 4;
-            int kernelRow = row / t_count;
-            return ref _buffer[kernelColumn + (KernelColumnLength * kernelRow)];
-        }
-
-        public override ref T UnsafeIndex(int column, int row)
-        {
-            int kernelColumn = column / 4, c = column % 4;
-            int kernelRow = row / t_count, r = row % t_count;
-            ref MatrixKernel<T> kernel = ref _buffer[kernelColumn + (KernelColumnLength * kernelRow)];
-            return ref kernel[c, r];
-        }
-
-        ~GCMatrix()
-        {
-            NativeMemory.AlignedFree(_buffer);
-        }
-
-        #region enumeration
-
-        public override unsafe MatrixSegmentEnumeration<T> ColumnEnumeration
-        {
-            [MethodImpl(MethodImplOptions.AggressiveInlining)]
-            get => new MatrixSegmentEnumeration<T>(_buffer, KernelColumnLength, KernelColumnLength * KernelRowLength, 1,
-                                                   KernelColumnLength);
-        }
-
-        public override unsafe MatrixSegmentEnumeration<T> GetRowEnumeration()
-        {
-            return new MatrixSegmentEnumeration<T>(_buffer, 1, KernelColumnLength, KernelColumnLength, KernelRowLength);
-        }
-
-        public override unsafe MatrixSegmentEnumeration<T> SequentialEnumeration
-        {
-            [MethodImpl(MethodImplOptions.AggressiveInlining)]
-            get => new MatrixSegmentEnumeration<T>(_buffer, KernelRowLength * KernelColumnLength,
-                                                   KernelColumnLength * KernelRowLength, 1,
-                                                   KernelRowLength * KernelColumnLength);
-        }
-
-        #endregion
-    }
-}
diff --git a/StgSharp.Common/Mathematics/Linear/Matrix_T.HLSF.cs b/StgSharp.Common/Mathematics/Linear/Matrix_T.HLSF.cs
deleted file mode 100644
index c0b28d22..00000000
--- a/StgSharp.Common/Mathematics/Linear/Matrix_T.HLSF.cs
+++ /dev/null
@@ -1,137 +0,0 @@
-//-----------------------------------------------------------------------
-// -----------------------------------------------------------------------
-// file="Matrix_T.HLSF"
-// Project: StgSharp
-// AuthorGroup: Nitload
-// Copyright (c) Nitload. All rights reserved.
-//     
-// Permission is hereby granted, free of charge, to any person obtaining a copy
-// of this software and associated documentation files (the "Software"), to deal
-// in the Software without restriction, including without limitation the rights
-// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
-// copies of the Software, and to permit persons to whom the Software is
-// furnished to do so, subject to the following conditions:
-//
-// The above copyright notice and this permission notice shall be included in all
-// copies or substantial portions of the Software.
-//
-// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
-// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
-// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
-// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
-// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
-// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
-// SOFTWARE.
-//     
-// -----------------------------------------------------------------------
-// -----------------------------------------------------------------------
-using StgSharp.HighPerformance;
-using System;
-using System.Collections.Generic;
-using System.Linq;
-using System.Numerics;
-using System.Runtime.CompilerServices;
-using System.Text;
-using System.Threading.Tasks;
-
-using hlsfAllocator = global::StgSharp.HighPerformance.Memory.HybridLayerSegregatedFitAllocator;
-using hlsfHandle = global::StgSharp.HighPerformance.Memory.HybridLayerSegregatedFitAllocationHandle;
-
-namespace StgSharp.Mathematics.Numeric
-{
-    internal unsafe partial class HlsfMatrix<T> : Matrix<T> where T : unmanaged, INumber<T>
-    {
-
-        private readonly MatrixKernel<T>* k_buffer;
-        private readonly hlsfAllocator allocator;
-        private readonly hlsfHandle handle;
-
-        internal HlsfMatrix(int column, int row, hlsfAllocator allocator)
-        {
-            KernelColumnLength = (column + 3) / 4;
-            KernelRowLength = (row + 3) / t_count;
-            ColumnLength = column;
-            RowLength = row;
-            long size = (long)KernelColumnLength * (long)KernelRowLength * (long)sizeof(MatrixKernel<T>);
-            this.handle = allocator.Alloc((uint)(size));
-            if (handle.AllocSize < size) {
-                throw new InsufficientMemoryException();
-            }
-            k_buffer = (MatrixKernel<T>*)handle.Pointer;
-        }
-
-        public override ref T this[int column, int row]
-        {
-            get
-            {
-                AssertIndex(column, row);
-                int kernelColumn = column / 4, c = column % 4;
-                int kernelRow = row / t_count, r = row % t_count;
-                ref MatrixKernel<T> kernel = ref k_buffer[(kernelColumn * kernelColumn) + kernelRow];
-                return ref kernel[c, r];
-            }
-        }
-
-        public override Matrix<T> this[
-                                  ReadOnlySpan<MatrixIndex> column,
-                                  ReadOnlySpan<MatrixIndex> row]
-        {
-            get => throw new NotImplementedException();
-            set => throw new NotImplementedException();
-        }
-
-        internal override unsafe MatrixKernel<T>* Buffer
-        {
-            [MethodImpl(MethodImplOptions.AggressiveInlining)]
-            get => k_buffer;
-        }
-
-        public override unsafe ref MatrixKernel<T> GetMatrixKernel(int column, int row)
-        {
-            AssertIndex(column, row);
-            int kernelColumn = column / 4, c = column % 4;
-            int kernelRow = row / t_count, r = row % t_count;
-            return ref k_buffer[(kernelColumn * kernelColumn) + kernelRow];
-        }
-
-        public override ref T UnsafeIndex(int column, int row)
-        {
-            int kernelColumn = column / 4, c = column % 4;
-            int kernelRow = row / t_count, r = row % t_count;
-            ref MatrixKernel<T> kernel = ref k_buffer[(kernelColumn * kernelColumn) + kernelRow];
-            return ref kernel[c, r];
-        }
-
-        ~HlsfMatrix()
-        {
-            allocator.Free(handle);
-        }
-
-        #region enumeration
-
-        public override unsafe MatrixSegmentEnumeration<T> ColumnEnumeration
-        {
-            [MethodImpl(MethodImplOptions.AggressiveInlining)]
-            get => new MatrixSegmentEnumeration<T>(k_buffer, KernelColumnLength,
-                                                   KernelColumnLength * KernelRowLength, 1,
-                                                   KernelColumnLength);
-        }
-
-        public override unsafe MatrixSegmentEnumeration<T> GetRowEnumeration()
-        {
-            return new MatrixSegmentEnumeration<T>(k_buffer, 1, KernelColumnLength,
-                                                   KernelColumnLength, KernelRowLength);
-        }
-
-        public override unsafe MatrixSegmentEnumeration<T> SequentialEnumeration
-        {
-            [MethodImpl(MethodImplOptions.AggressiveInlining)]
-
-            get => new MatrixSegmentEnumeration<T>(k_buffer, KernelRowLength * KernelColumnLength,
-                                                   KernelColumnLength * KernelRowLength, 1,
-                                                   KernelRowLength * KernelColumnLength);
-        }
-
-        #endregion
-    }
-}
diff --git a/StgSharp.Common/Mathematics/Linear/Matrix_T.cs b/StgSharp.Common/Mathematics/Linear/Matrix_T.cs
deleted file mode 100644
index 3d1e3cff..00000000
--- a/StgSharp.Common/Mathematics/Linear/Matrix_T.cs
+++ /dev/null
@@ -1,218 +0,0 @@
-//-----------------------------------------------------------------------
-// -----------------------------------------------------------------------
-// file="Matrix_T"
-// Project: StgSharp
-// AuthorGroup: Nitload
-// Copyright (c) Nitload. All rights reserved.
-//     
-// Permission is hereby granted, free of charge, to any person obtaining a copy
-// of this software and associated documentation files (the "Software"), to deal
-// in the Software without restriction, including without limitation the rights
-// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
-// copies of the Software, and to permit persons to whom the Software is
-// furnished to do so, subject to the following conditions:
-//
-// The above copyright notice and this permission notice shall be included in all
-// copies or substantial portions of the Software.
-//
-// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
-// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
-// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
-// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
-// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
-// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
-// SOFTWARE.
-//     
-// -----------------------------------------------------------------------
-// -----------------------------------------------------------------------
-using StgSharp.HighPerformance;
-using System;
-using System.Numerics;
-using System.Runtime.CompilerServices;
-using System.Runtime.InteropServices;
-
-// using hlsfHandle = global::StgSharp.HighPerformance.Memory.HybridLayerSegregatedFitAllocationHandle;
-
-namespace StgSharp.Mathematics.Numeric
-{
-    public abstract unsafe partial class Matrix<T> where T : unmanaged, INumber<T>
-    {
-
-        private protected readonly int t_count = 16 / sizeof(T);
-
-        private protected readonly int t_size = sizeof(T);
-
-        private protected Matrix() { }
-
-        public abstract ref T this[int column, int row]
-        {
-            get;
-        }
-
-        public abstract unsafe Matrix<T> this[ReadOnlySpan<MatrixIndex> column, ReadOnlySpan<MatrixIndex> row]
-        {
-            get;
-            set;
-        }
-
-        /// <summary>
-        ///   Length of the matrix in columns.
-        /// </summary>
-        public int ColumnLength { get; init; }
-
-        /// <summary>
-        ///   Length of the matrix in rows.
-        /// </summary>
-        public int RowLength { get; init; }
-
-        public abstract MatrixSegmentEnumeration<T> ColumnEnumeration { get; }
-
-        public abstract MatrixSegmentEnumeration<T> SequentialEnumeration { get; }
-
-        internal abstract MatrixKernel<T>* Buffer { get; }
-
-        protected internal int KernelColumnLength { get; init; }
-
-        protected internal int KernelRowLength { get; init; }
-
-        public abstract ref MatrixKernel<T> GetMatrixKernel(int column, int row);
-
-        public abstract MatrixSegmentEnumeration<T> GetRowEnumeration();
-
-        [Obsolete("This method does not contain boarder check, so be careful on size or use indexer instead.", false)]
-        public abstract ref T UnsafeIndex(int column, int row);
-
-        private protected void AssertIndex(int column, int row)
-        {
-            if (column < 0 || column >= ColumnLength) {
-                throw new ArgumentOutOfRangeException(nameof(column));
-            }
-
-            if (row < 0 || row >= RowLength) {
-                throw new ArgumentOutOfRangeException(nameof(row));
-            }
-        }
-
-    }
-
-    public readonly unsafe ref struct MatrixSegmentEnumeration<T>(
-                                      MatrixKernel<T>* source,
-                                      int primStride,
-                                      int primSize,
-                                      int secondaryStride,
-                                      int secondarySize,
-                                      int primOffset = 0,
-                                      int secondaryOffset = 0)
-        where T : unmanaged, INumber<T>
-    {
-
-        private readonly MatrixKernel<T>* _source = source;
-        internal readonly int PrimOffset = primOffset;
-
-        internal readonly int PrimSize = primSize;
-        internal readonly int PrimStride = primStride;
-        internal readonly int SecondaryOffset = secondaryOffset;
-        internal readonly int SecondarySize = secondarySize;
-        internal readonly int SecondaryStride = secondaryStride;
-
-        internal readonly MatrixKernel<T>* Source
-        {
-            [MethodImpl(MethodImplOptions.AggressiveInlining)]
-            get => _source;
-        }
-
-        public Enumerator GetEnumerator()
-        {
-            return new Enumerator(in this);
-        }
-
-        public ref struct Enumerator(in MatrixSegmentEnumeration<T> enumeration)
-        {
-
-            private readonly MatrixKernel<T>* _source = enumeration._source;
-            private int _indexCount = -1;
-            private readonly int _stride = enumeration.PrimStride;
-            private readonly long _bound = (long)enumeration.PrimSize * enumeration.PrimStride;
-            private long _index = (long)enumeration.PrimOffset * enumeration.PrimStride;
-
-            private readonly MatrixSegmentEnumeration<T> _enumeration;
-
-            public readonly MatrixSegment<T> Current
-            {
-                [MethodImpl(MethodImplOptions.AggressiveInlining)]
-                get => new(_source + _index, _enumeration.SecondarySize, _enumeration.SecondaryStride,
-                           _enumeration.PrimOffset);
-            }
-
-            public bool MoveNext()
-            {
-                _indexCount++;
-                _index += _stride;
-                if (_index >= _bound) {
-                    _index = 0;
-                }
-                return _indexCount >= _enumeration.PrimSize;
-            }
-
-        }
-
-    }
-
-    public readonly unsafe ref struct MatrixSegment<T>(MatrixKernel<T>* source, int size, int stride, int offset)
-        where T : unmanaged, INumber<T>
-    {
-
-        private readonly MatrixKernel<T>* _source = source;
-        private readonly int _offset = offset;
-        private readonly int _secondarySize = size;
-        private readonly int _size = size;
-        private readonly int _stride = stride;
-
-        public ref MatrixKernel<T> this[int index]
-        {
-            get
-            {
-                if (index < 0 || index >= _size) {
-                    throw new ArgumentOutOfRangeException(nameof(index));
-                }
-                return ref _source[index * _stride];
-            }
-        }
-
-        [MethodImpl(MethodImplOptions.AggressiveInlining)]
-        public Enumerator GetEnumerator()
-        {
-            return new Enumerator(in this);
-        }
-
-        public ref struct Enumerator(in MatrixSegment<T> segment)
-        {
-
-            private readonly int _end = segment._size;
-
-            private int _indexCount = -1;
-            private readonly long _bound = (long)segment._size * segment._stride;
-            private long _index = (long)segment._offset * segment._stride;
-            private readonly MatrixSegment<T> _segment = segment;
-
-            public readonly MatrixKernel<T>* Current
-            {
-                [MethodImpl(MethodImplOptions.AggressiveInlining)]
-                get => _segment._source + _index;
-            }
-
-            public bool MoveNext()
-            {
-                _index += _segment._stride;
-                _indexCount++;
-                if (_index >= _bound) {
-                    _index = 0;
-                }
-
-                return _indexCount < _end;
-            }
-
-        }
-
-    }
-}
diff --git a/StgSharp.Mathematics/Numeric/MatrixCompute.Factorize.cs b/StgSharp.Mathematics/Numeric/MatrixCompute.Factorize.cs
index ebc58bdd..bc4a4d1c 100644
--- a/StgSharp.Mathematics/Numeric/MatrixCompute.Factorize.cs
+++ b/StgSharp.Mathematics/Numeric/MatrixCompute.Factorize.cs
@@ -38,17 +38,69 @@ namespace StgSharp.Mathematics.Numeric
 
         public static void FactorizePLU(
                            Matrix<float> matrix,
-                           Matrix<float> p,
+                           Span<float> pivot,
                            Matrix<float> lower,
                            Matrix<float> upper)
         {
             if (matrix.ColumnLength != matrix.RowLength) {
                 throw new InvalidOperationException("Matrix must be square.");
             }
+            if (matrix.Layout != MatrixLayout.DenseRectangle) {
+                throw new NotSupportedException("Only dense square matrices are supported.");
+            }
+            int n = matrix.RowLength;
+            if (pivot.Length < n) {
+                throw new ArgumentException("Pivot span length is insufficient.", nameof(pivot));
+            }
+            if (lower.RowLength != n ||
+                lower.ColumnLength != n ||
+                lower.Layout != MatrixLayout.LowerTriangle) {
+                throw new ArgumentException("Lower matrix must be lower-triangular with same dimensions as input.", nameof(lower));
+            }
+            if (upper.RowLength != n ||
+                upper.ColumnLength != n ||
+                upper.Layout != MatrixLayout.UpperTriangle) {
+                throw new ArgumentException("Upper matrix must be upper-triangular with same dimensions as input.", nameof(upper));
+            }
+
             int size = matrix.KernelColumnLength * matrix.KernelRowLength;
             if (size < 256)
             {
-                for (int i = 0; i < matrix.KernelColumnLength; i++) { }
+                // Naive Doolittle-style PLU without row swaps (for illustration).
+                for (int i = 0; i < n; i++)
+                {
+                    pivot[i] = i;          // identity pivot
+                    lower[i, i] = 1.0f;    // unit diagonal for L
+                }
+
+                for (int k = 0; k < n; k++)
+                {
+                    // Compute U[k, j] for j >= k
+                    for (int j = k; j < n; j++)
+                    {
+                        float sum = 0f;
+                        for (int s = 0; s < k; s++) {
+                            sum += lower[k, s] * upper[s, j];
+                        }
+                        upper[k, j] = matrix[k, j] - sum;
+                    }
+
+                    // Compute L[i, k] for i > k
+                    for (int i = k + 1; i < n; i++)
+                    {
+                        float sum = 0f;
+                        for (int s = 0; s < k; s++) {
+                            sum += lower[i, s] * upper[s, k];
+                        }
+                        float u = upper[k, k];
+                        if (u == 0f) {
+                            throw new InvalidOperationException("Zero pivot encountered in demonstration PLU.");
+                        }
+                        lower[i, k] = (matrix.GetElementUnsafe(i, k) - sum) / u;
+                    }
+                }
+
+                // TODO: For larger kernels, consider calling native pivot helper to extract 4 pivots at once.
             } else if (size < 1024) { } else { }
         }
 
diff --git a/StgSharp.Mathematics/Numeric/MatrixCompute.cs b/StgSharp.Mathematics/Numeric/MatrixCompute.cs
index 766dbd2c..cc66b7a2 100644
--- a/StgSharp.Mathematics/Numeric/MatrixCompute.cs
+++ b/StgSharp.Mathematics/Numeric/MatrixCompute.cs
@@ -198,6 +198,10 @@ namespace StgSharp.Mathematics.Numeric
             if (left.ColumnLength != ans.ColumnLength || left.RowLength != ans.RowLength) {
                 throw new IndexOutOfRangeException("Matrix dimensions must agree.");
             }
+            if (left.Layout != MatrixLayout.DenseRectangle ||
+                ans.Layout != MatrixLayout.DenseRectangle) {
+                throw new NotSupportedException("Only dense rectangle matrices are supported.");
+            }
             long count = (long)left.KernelColumnLength * left.KernelRowLength;
             ScalarPacket* scalar = MatrixParallelFactory.CreateScalarPacket();
             scalar->Data<float>(0) = right;
@@ -243,6 +247,11 @@ namespace StgSharp.Mathematics.Numeric
                 left.RowLength != ans.RowLength) {
                 throw new IndexOutOfRangeException("Matrix dimensions must agree.");
             }
+            if (left.Layout != MatrixLayout.DenseRectangle ||
+                right.Layout != MatrixLayout.DenseRectangle ||
+                ans.Layout != MatrixLayout.DenseRectangle) {
+                throw new NotSupportedException("Only dense rectangle matrices are supported.");
+            }
             long count = (long)left.KernelColumnLength * left.KernelRowLength;
             if (count <= 256)
             {
diff --git a/StgSharp.Native/sn-src/k_pivot.c b/StgSharp.Native/sn-src/k_pivot.c
index 6617c14b..c2b51c7b 100644
--- a/StgSharp.Native/sn-src/k_pivot.c
+++ b/StgSharp.Native/sn-src/k_pivot.c
@@ -2,7 +2,7 @@
 
 // Hybrid implementation: SIMD for Abs, Scalar for Max
 // Assumes Column-Major layout for both MAT_KERNEL content and Kernel sequence
-static void povit_float_simd_abs(MAT_KERNEL(float) const *source, size_t col_begin,
+static void povit_float(MAT_KERNEL(float) const *source, size_t col_begin,
                                  size_t col_length, size_t *restrict ans)
 {
         float max_v[4] = { -1.0f, -1.0f, -1.0f, -1.0f };
@@ -62,18 +62,3 @@ static void povit_float_simd_abs(MAT_KERNEL(float) const *source, size_t col_beg
                 }
         }
 }
-
-DECLARE_MAT_POVIT_PROC(float, sse)
-{
-        povit_float_simd_abs(source, col_begin, col_length, ans);
-}
-
-DECLARE_MAT_POVIT_PROC(float, avx)
-{
-        povit_float_simd_abs(source, col_begin, col_length, ans);
-}
-
-DECLARE_MAT_POVIT_PROC(float, 512)
-{
-        povit_float_simd_abs(source, col_begin, col_length, ans);
-}
diff --git a/StgSharpDebug/Program.cs b/StgSharpDebug/Program.cs
index bbae7ad6..f21e8f8b 100644
--- a/StgSharpDebug/Program.cs
+++ b/StgSharpDebug/Program.cs
@@ -58,11 +58,11 @@ namespace StgSharp
                 unchecked {
                     hlsf = new((nuint)(64 * (ulong)10000 * 10000));
                 }
-                Matrix<float> m = Matrix.FromHlsf<float>(4000, 4000, hlsf);
+                Matrix<float> m = Matrix<float>.Create(4000, 4000, MatrixLayout.DenseRectangle, hlsf);
                 MatrixCompute.Fill(m, 1.0f);
-                Matrix<float> n = Matrix.FromHlsf<float>(4000, 4000, hlsf);
+                Matrix<float> n = Matrix<float>.Create(4000, 4000, MatrixLayout.DenseRectangle, hlsf);
                 MatrixCompute.Fill(n, 1.0f);
-                Matrix<float> p = Matrix.FromHlsf<float>(4000, 4000, hlsf);
+                Matrix<float> p = Matrix<float>.Create(4000, 4000, MatrixLayout.DenseRectangle, hlsf);
 
                 // MatrixCompute.Fill(p, 0.0f);
                 /*
diff --git a/StgSharpDevelop.sln b/StgSharpDevelop.sln
index 1811afab..e099905a 100644
--- a/StgSharpDevelop.sln
+++ b/StgSharpDevelop.sln
@@ -46,8 +46,8 @@ Global
 		{3EAF2EE6-FA9E-4F57-951F-7E6F8125DFBF}.Debug|x64.Build.0 = Debug|x64
 		{3EAF2EE6-FA9E-4F57-951F-7E6F8125DFBF}.PerformanceDebug|ARM64.ActiveCfg = PerformanceDebug|ARM64
 		{3EAF2EE6-FA9E-4F57-951F-7E6F8125DFBF}.PerformanceDebug|ARM64.Build.0 = PerformanceDebug|ARM64
-		{3EAF2EE6-FA9E-4F57-951F-7E6F8125DFBF}.PerformanceDebug|x64.ActiveCfg = PerformanceDebug|x64
-		{3EAF2EE6-FA9E-4F57-951F-7E6F8125DFBF}.PerformanceDebug|x64.Build.0 = PerformanceDebug|x64
+		{3EAF2EE6-FA9E-4F57-951F-7E6F8125DFBF}.PerformanceDebug|x64.ActiveCfg = Release|x64
+		{3EAF2EE6-FA9E-4F57-951F-7E6F8125DFBF}.PerformanceDebug|x64.Build.0 = Release|x64
 		{3EAF2EE6-FA9E-4F57-951F-7E6F8125DFBF}.Release|ARM64.ActiveCfg = Release|ARM64
 		{3EAF2EE6-FA9E-4F57-951F-7E6F8125DFBF}.Release|ARM64.Build.0 = Release|ARM64
 		{3EAF2EE6-FA9E-4F57-951F-7E6F8125DFBF}.Release|x64.ActiveCfg = Release|x64
@@ -58,8 +58,8 @@ Global
 		{610B992B-BB34-49C3-9993-676C595FC12E}.Debug|x64.Build.0 = Debug|x64
 		{610B992B-BB34-49C3-9993-676C595FC12E}.PerformanceDebug|ARM64.ActiveCfg = PerformanceDebug|ARM64
 		{610B992B-BB34-49C3-9993-676C595FC12E}.PerformanceDebug|ARM64.Build.0 = PerformanceDebug|ARM64
-		{610B992B-BB34-49C3-9993-676C595FC12E}.PerformanceDebug|x64.ActiveCfg = PerformanceDebug|x64
-		{610B992B-BB34-49C3-9993-676C595FC12E}.PerformanceDebug|x64.Build.0 = PerformanceDebug|x64
+		{610B992B-BB34-49C3-9993-676C595FC12E}.PerformanceDebug|x64.ActiveCfg = Release|x64
+		{610B992B-BB34-49C3-9993-676C595FC12E}.PerformanceDebug|x64.Build.0 = Release|x64
 		{610B992B-BB34-49C3-9993-676C595FC12E}.Release|ARM64.ActiveCfg = Release|ARM64
 		{610B992B-BB34-49C3-9993-676C595FC12E}.Release|ARM64.Build.0 = Release|ARM64
 		{610B992B-BB34-49C3-9993-676C595FC12E}.Release|x64.ActiveCfg = Release|x64
@@ -69,8 +69,8 @@ Global
 		{20CBFF26-6746-402E-992C-7B643E9423EB}.Debug|x64.Build.0 = Debug|x64
 		{20CBFF26-6746-402E-992C-7B643E9423EB}.PerformanceDebug|ARM64.ActiveCfg = PerformanceDebug|x64
 		{20CBFF26-6746-402E-992C-7B643E9423EB}.PerformanceDebug|ARM64.Build.0 = PerformanceDebug|x64
-		{20CBFF26-6746-402E-992C-7B643E9423EB}.PerformanceDebug|x64.ActiveCfg = PerformanceDebug|x64
-		{20CBFF26-6746-402E-992C-7B643E9423EB}.PerformanceDebug|x64.Build.0 = PerformanceDebug|x64
+		{20CBFF26-6746-402E-992C-7B643E9423EB}.PerformanceDebug|x64.ActiveCfg = Release|x64
+		{20CBFF26-6746-402E-992C-7B643E9423EB}.PerformanceDebug|x64.Build.0 = Release|x64
 		{20CBFF26-6746-402E-992C-7B643E9423EB}.Release|ARM64.ActiveCfg = Release|ARM64
 		{20CBFF26-6746-402E-992C-7B643E9423EB}.Release|ARM64.Build.0 = Release|ARM64
 		{20CBFF26-6746-402E-992C-7B643E9423EB}.Release|x64.ActiveCfg = Release|x64
@@ -81,8 +81,8 @@ Global
 		{10B5819F-2A62-41B6-980A-EB9E76A0E95C}.Debug|x64.Build.0 = Debug|x64
 		{10B5819F-2A62-41B6-980A-EB9E76A0E95C}.PerformanceDebug|ARM64.ActiveCfg = PerformanceDebug|x64
 		{10B5819F-2A62-41B6-980A-EB9E76A0E95C}.PerformanceDebug|ARM64.Build.0 = PerformanceDebug|x64
-		{10B5819F-2A62-41B6-980A-EB9E76A0E95C}.PerformanceDebug|x64.ActiveCfg = PerformanceDebug|x64
-		{10B5819F-2A62-41B6-980A-EB9E76A0E95C}.PerformanceDebug|x64.Build.0 = PerformanceDebug|x64
+		{10B5819F-2A62-41B6-980A-EB9E76A0E95C}.PerformanceDebug|x64.ActiveCfg = Release|x64
+		{10B5819F-2A62-41B6-980A-EB9E76A0E95C}.PerformanceDebug|x64.Build.0 = Release|x64
 		{10B5819F-2A62-41B6-980A-EB9E76A0E95C}.Release|ARM64.ActiveCfg = Release|x64
 		{10B5819F-2A62-41B6-980A-EB9E76A0E95C}.Release|ARM64.Build.0 = Release|x64
 		{10B5819F-2A62-41B6-980A-EB9E76A0E95C}.Release|x64.ActiveCfg = Release|x64
@@ -93,8 +93,8 @@ Global
 		{5B51F5EA-138C-46B5-B36F-1D389968B6CF}.Debug|x64.Build.0 = Debug|x64
 		{5B51F5EA-138C-46B5-B36F-1D389968B6CF}.PerformanceDebug|ARM64.ActiveCfg = PerformanceDebug|x64
 		{5B51F5EA-138C-46B5-B36F-1D389968B6CF}.PerformanceDebug|ARM64.Build.0 = PerformanceDebug|x64
-		{5B51F5EA-138C-46B5-B36F-1D389968B6CF}.PerformanceDebug|x64.ActiveCfg = PerformanceDebug|x64
-		{5B51F5EA-138C-46B5-B36F-1D389968B6CF}.PerformanceDebug|x64.Build.0 = PerformanceDebug|x64
+		{5B51F5EA-138C-46B5-B36F-1D389968B6CF}.PerformanceDebug|x64.ActiveCfg = Release|x64
+		{5B51F5EA-138C-46B5-B36F-1D389968B6CF}.PerformanceDebug|x64.Build.0 = Release|x64
 		{5B51F5EA-138C-46B5-B36F-1D389968B6CF}.Release|ARM64.ActiveCfg = Release|x64
 		{5B51F5EA-138C-46B5-B36F-1D389968B6CF}.Release|ARM64.Build.0 = Release|x64
 		{5B51F5EA-138C-46B5-B36F-1D389968B6CF}.Release|x64.ActiveCfg = Release|x64
@@ -105,8 +105,8 @@ Global
 		{D9538DE0-EE4C-4183-86D6-7DFC08A7BDFB}.Debug|x64.Build.0 = Debug|x64
 		{D9538DE0-EE4C-4183-86D6-7DFC08A7BDFB}.PerformanceDebug|ARM64.ActiveCfg = PerformanceDebug|x64
 		{D9538DE0-EE4C-4183-86D6-7DFC08A7BDFB}.PerformanceDebug|ARM64.Build.0 = PerformanceDebug|x64
-		{D9538DE0-EE4C-4183-86D6-7DFC08A7BDFB}.PerformanceDebug|x64.ActiveCfg = PerformanceDebug|x64
-		{D9538DE0-EE4C-4183-86D6-7DFC08A7BDFB}.PerformanceDebug|x64.Build.0 = PerformanceDebug|x64
+		{D9538DE0-EE4C-4183-86D6-7DFC08A7BDFB}.PerformanceDebug|x64.ActiveCfg = Release|x64
+		{D9538DE0-EE4C-4183-86D6-7DFC08A7BDFB}.PerformanceDebug|x64.Build.0 = Release|x64
 		{D9538DE0-EE4C-4183-86D6-7DFC08A7BDFB}.Release|ARM64.ActiveCfg = Release|ARM64
 		{D9538DE0-EE4C-4183-86D6-7DFC08A7BDFB}.Release|ARM64.Build.0 = Release|ARM64
 		{D9538DE0-EE4C-4183-86D6-7DFC08A7BDFB}.Release|x64.ActiveCfg = Release|x64
@@ -117,8 +117,8 @@ Global
 		{9946599F-4D34-440F-840D-F9443D5AEFAA}.Debug|x64.Build.0 = Debug|x64
 		{9946599F-4D34-440F-840D-F9443D5AEFAA}.PerformanceDebug|ARM64.ActiveCfg = PerformanceDebug|ARM64
 		{9946599F-4D34-440F-840D-F9443D5AEFAA}.PerformanceDebug|ARM64.Build.0 = PerformanceDebug|ARM64
-		{9946599F-4D34-440F-840D-F9443D5AEFAA}.PerformanceDebug|x64.ActiveCfg = PerformanceDebug|x64
-		{9946599F-4D34-440F-840D-F9443D5AEFAA}.PerformanceDebug|x64.Build.0 = PerformanceDebug|x64
+		{9946599F-4D34-440F-840D-F9443D5AEFAA}.PerformanceDebug|x64.ActiveCfg = Release|x64
+		{9946599F-4D34-440F-840D-F9443D5AEFAA}.PerformanceDebug|x64.Build.0 = Release|x64
 		{9946599F-4D34-440F-840D-F9443D5AEFAA}.Release|ARM64.ActiveCfg = Release|ARM64
 		{9946599F-4D34-440F-840D-F9443D5AEFAA}.Release|ARM64.Build.0 = Release|ARM64
 		{9946599F-4D34-440F-840D-F9443D5AEFAA}.Release|x64.ActiveCfg = Release|x64