diff --git a/src/Numerics/LinearAlgebra/Matrix.Slice.cs b/src/Numerics/LinearAlgebra/Matrix.Slice.cs
new file mode 100644
index 00000000..1797b2fe
--- /dev/null
+++ b/src/Numerics/LinearAlgebra/Matrix.Slice.cs
@@ -0,0 +1,175 @@
+using System;
+
+namespace MathNet.Numerics.LinearAlgebra
+{
+    /// <summary>
+    /// This class is used for slice Matrix by using System.Range.
+    /// It is different from System.Range functions in the use of ".." syntax.
+    /// Because the when use ".." in array,like double[],the sliced array won't contain the end index.
+    /// However,in this Matrix<T>,it will contain the end index.
+    /// </summary>
+    /// <typeparam name="T"></typeparam>
+    public abstract partial class Matrix<T>
+    {
+        /// <summary>
+        /// Get or Set the SubMatrix by [Range,Range]
+        /// For example:
+        ///        Matrix<double> mat = Matrix<double>.Build.Dense(10,10);
+        ///        mat[1..2,2..3];
+        ///        mat[1..2,^9..^1];
+        ///        mat[..,2..3];
+        ///        mat[1..2,2..3] = a new Matrix has the same dimension with this submatrix;      
+        /// </summary>
+        /// <param name="rowRange">the Row Range,it must contain more than one Row</param>
+        /// <param name="columnRange">the Column Range,it must contain more than one Column</param>
+        /// <returns>A SubMatrix</returns>
+        public Matrix<T> this[Range rowRange, Range columnRange]
+        {
+            get
+            {
+                int rowStartIndex = rowRange.Start.IsFromEnd ? RowCount - rowRange.Start.Value - 1 : rowRange.Start.Value;
+                int rowEndIndex = rowRange.End.IsFromEnd ? RowCount - rowRange.End.Value - 1 : rowRange.End.Value;
+                int rowCount = rowEndIndex - rowStartIndex + 1;
+
+                if (rowCount <=1 || rowCount > RowCount)
+                {
+                    throw new ArgumentException($"The argument Row Range:{rowRange} is wrong!");
+                }
+
+                int columnStartIndex = columnRange.Start.IsFromEnd ? ColumnCount - columnRange.Start.Value - 1 : columnRange.Start.Value;
+                int columnEndIndex = columnRange.End.IsFromEnd ? ColumnCount - columnRange.End.Value - 1 : columnRange.End.Value;
+                int columnCount = columnEndIndex - columnStartIndex + 1;
+
+                if (columnCount <= 1 || columnCount > ColumnCount)
+                {
+                    throw new ArgumentException($"The argument Column Range:{columnRange} is wrong!");
+                }
+
+                var result = Build.SameAs(this, rowCount, columnCount);
+                Storage.CopySubMatrixTo(result.Storage, rowStartIndex, 0, rowCount, columnStartIndex, 0, columnCount, ExistingData.AssumeZeros);
+                return result;
+            }
+
+            set
+            {
+                int rowStartIndex = rowRange.Start.IsFromEnd ? RowCount - rowRange.Start.Value - 1 : rowRange.Start.Value;
+                int rowEndIndex = rowRange.End.IsFromEnd ? RowCount - rowRange.End.Value - 1 : rowRange.End.Value;
+                int rowCount = rowEndIndex - rowStartIndex + 1;
+
+                if (rowCount <= 1 || rowCount > RowCount)
+                {
+                    throw new ArgumentException($"The argument Row Range:{rowRange} is wrong!");
+                }
+
+                int columnStartIndex = columnRange.Start.IsFromEnd ? ColumnCount - columnRange.Start.Value - 1 : columnRange.Start.Value;
+                int columnEndIndex = columnRange.End.IsFromEnd ? ColumnCount - columnRange.End.Value - 1 : columnRange.End.Value;
+                int columnCount = columnEndIndex - columnStartIndex + 1;
+
+                if (columnCount <= 1 || columnCount > ColumnCount)
+                {
+                    throw new ArgumentException($"The argument Column Range:{columnRange} is wrong!");
+                }
+
+                value.Storage.CopySubMatrixTo(Storage, 0, rowStartIndex, rowCount, 0, columnStartIndex, columnCount);
+            }
+        }
+
+        /// <summary>
+        /// Get or Set the Column SubVector of the Matrix 
+        /// </summary>
+        /// <param name="rowRange">the Row Range,it must contain more than one Row</param>
+        /// <param name="columnIndex">the column index</param>
+        /// <returns>a vector</returns>
+        public Vector<T> this[Range rowRange, int columnIndex]
+        {
+            get
+            {
+                int rowStartIndex = rowRange.Start.IsFromEnd ? RowCount - rowRange.Start.Value - 1 : rowRange.Start.Value;
+                int rowEndIndex = rowRange.End.IsFromEnd ? RowCount - rowRange.End.Value - 1 : rowRange.End.Value;
+                int rowCount = rowEndIndex - rowStartIndex + 1;
+
+                if (rowCount <= 1 || rowCount > RowCount)
+                {
+                    throw new ArgumentException($"The argument Row Range:{rowRange} is wrong!");
+                }
+
+                if ((uint)columnIndex >= (uint)ColumnCount)
+                {
+                    throw new ArgumentOutOfRangeException(nameof(columnIndex));
+                }
+
+                var ret = Vector<T>.Build.SameAs(this, rowCount);
+                Storage.CopySubColumnTo(ret.Storage, columnIndex, rowStartIndex, 0, rowCount);
+                return ret;
+            }
+
+            set
+            {
+                int rowStartIndex = rowRange.Start.IsFromEnd ? RowCount - rowRange.Start.Value - 1 : rowRange.Start.Value;
+                int rowEndIndex = rowRange.End.IsFromEnd ? RowCount - rowRange.End.Value - 1 : rowRange.End.Value;
+                int rowCount = rowEndIndex - rowStartIndex + 1;
+
+                if (rowCount <= 1 || rowCount > RowCount)
+                {
+                    throw new ArgumentException($"The argument Row Range:{rowRange} is wrong!");
+                }
+
+                if ((uint)columnIndex >= (uint)ColumnCount)
+                {
+                    throw new ArgumentOutOfRangeException(nameof(columnIndex));
+                }
+
+                value.Storage.CopyToSubColumn(Storage, columnIndex, 0, rowStartIndex, rowCount);
+            }
+        }
+
+        /// <summary>
+        /// Get or Set the row SubVector of the Matrix 
+        /// </summary>
+        /// <param name="rowIndex">the column index</param>
+        /// <param name="columnRange">the Column Range,it must contain more than one Column</param>
+        /// <returns>a vector</returns>
+        public Vector<T> this[int rowIndex, Range columnRange]
+        {
+            get
+            {
+                int columnStartIndex = columnRange.Start.IsFromEnd ? ColumnCount - columnRange.Start.Value - 1 : columnRange.Start.Value;
+                int columnEndIndex = columnRange.End.IsFromEnd ? ColumnCount - columnRange.End.Value - 1 : columnRange.End.Value;
+                int columnCount = columnEndIndex - columnStartIndex + 1;
+
+                if (columnCount <= 1 || columnCount > ColumnCount)
+                {
+                    throw new ArgumentException($"The argument Column Range:{columnRange} is wrong!");
+                }
+
+                if ((uint)rowIndex >= (uint)RowCount)
+                {
+                    throw new ArgumentOutOfRangeException(nameof(rowIndex));
+                }
+
+                var ret = Vector<T>.Build.SameAs(this, columnCount);
+                Storage.CopySubRowTo(ret.Storage, rowIndex, columnStartIndex, 0, columnCount);
+                return ret;
+            }
+
+            set
+            {
+                int columnStartIndex = columnRange.Start.IsFromEnd ? ColumnCount - columnRange.Start.Value - 1 : columnRange.Start.Value;
+                int columnEndIndex = columnRange.End.IsFromEnd ? ColumnCount - columnRange.End.Value - 1 : columnRange.End.Value;
+                int columnCount = columnEndIndex - columnStartIndex + 1;
+
+                if (columnCount <= 1 || columnCount > ColumnCount)
+                {
+                    throw new ArgumentException($"The argument Column Range:{columnRange} is wrong!");
+                }
+
+                if ((uint)rowIndex >= (uint)RowCount)
+                {
+                    throw new ArgumentOutOfRangeException(nameof(rowIndex));
+                }
+
+                value.Storage.CopyToSubRow(Storage, rowIndex, 0, columnStartIndex, columnCount);
+            }
+        }
+    }
+}