diff --git a/src/Numerics/LinearAlgebra/Storage/DenseColumnMajorMatrixStorage.cs b/src/Numerics/LinearAlgebra/Storage/DenseColumnMajorMatrixStorage.cs
index 90c6bafa..0312a85a 100644
--- a/src/Numerics/LinearAlgebra/Storage/DenseColumnMajorMatrixStorage.cs
+++ b/src/Numerics/LinearAlgebra/Storage/DenseColumnMajorMatrixStorage.cs
@@ -595,6 +595,20 @@ namespace MathNet.Numerics.LinearAlgebra.Storage
             target.Values = values.ToArray();
         }
 
+        internal override void TransposeSquareInplaceUnchecked()
+        {
+            for (var j = 0; j < ColumnCount; j++)
+            {
+                var index = j * RowCount;
+                for (var i = 0; i < j; i++)
+                {
+                    T swap = Data[index + i];
+                    Data[index + i] = Data[i*ColumnCount + j];
+                    Data[i*ColumnCount + j] = swap;
+                }
+            }
+        }
+
         // EXTRACT
 
         public override T[] ToRowMajorArray()
diff --git a/src/Numerics/LinearAlgebra/Storage/DiagonalMatrixStorage.cs b/src/Numerics/LinearAlgebra/Storage/DiagonalMatrixStorage.cs
index 05ae5191..58a315bd 100644
--- a/src/Numerics/LinearAlgebra/Storage/DiagonalMatrixStorage.cs
+++ b/src/Numerics/LinearAlgebra/Storage/DiagonalMatrixStorage.cs
@@ -491,6 +491,11 @@ namespace MathNet.Numerics.LinearAlgebra.Storage
             CopyToUnchecked(target, existingData);
         }
 
+        internal override void TransposeSquareInplaceUnchecked()
+        {
+            // nothing to do
+        }
+
         // EXTRACT
 
         public override T[] ToRowMajorArray()
diff --git a/src/Numerics/LinearAlgebra/Storage/MatrixStorage.cs b/src/Numerics/LinearAlgebra/Storage/MatrixStorage.cs
index 3f3f14e7..b8c65143 100644
--- a/src/Numerics/LinearAlgebra/Storage/MatrixStorage.cs
+++ b/src/Numerics/LinearAlgebra/Storage/MatrixStorage.cs
@@ -467,17 +467,18 @@ namespace MathNet.Numerics.LinearAlgebra.Storage
                 throw new ArgumentNullException("target");
             }
 
-            if (ReferenceEquals(this, target))
-            {
-                throw new NotSupportedException("In-place transpose is not supported.");
-            }
-
             if (RowCount != target.ColumnCount || ColumnCount != target.RowCount)
             {
                 var message = string.Format(Resources.ArgumentMatrixDimensions2, RowCount + "x" + ColumnCount, target.RowCount + "x" + target.ColumnCount);
                 throw new ArgumentException(message, "target");
             }
 
+            if (ReferenceEquals(this, target))
+            {
+                TransposeSquareInplaceUnchecked();
+                return;
+            }
+
             TransposeToUnchecked(target, existingData);
         }
 
@@ -492,6 +493,19 @@ namespace MathNet.Numerics.LinearAlgebra.Storage
             }
         }
 
+        internal virtual void TransposeSquareInplaceUnchecked()
+        {
+            for (int j = 0; j < ColumnCount; j++)
+            {
+                for (int i = 0; i < j; i++)
+                {
+                    T swap = At(i, j);
+                    At(i, j, At(j, i));
+                    At(j, i, swap);
+                }
+            }
+        }
+
         // EXTRACT
 
         public virtual T[] ToRowMajorArray()
diff --git a/src/Numerics/LinearAlgebra/Storage/SparseCompressedRowMatrixStorage.cs b/src/Numerics/LinearAlgebra/Storage/SparseCompressedRowMatrixStorage.cs
index 840269e3..c5e29c31 100644
--- a/src/Numerics/LinearAlgebra/Storage/SparseCompressedRowMatrixStorage.cs
+++ b/src/Numerics/LinearAlgebra/Storage/SparseCompressedRowMatrixStorage.cs
@@ -1154,6 +1154,46 @@ namespace MathNet.Numerics.LinearAlgebra.Storage
             }
         }
 
+        internal override void TransposeSquareInplaceUnchecked()
+        {
+            var cx = new T[ValueCount]; //target.Values;
+            var cp = new int[RowCount + 1];
+            var ci = new int[ValueCount]; //target.ColumnIndices;
+
+            // Column counts
+            int[] w = new int[ColumnCount];
+            for (int p = 0; p < RowPointers[RowCount]; p++)
+            {
+                w[ColumnIndices[p]]++;
+            }
+
+            // Column pointers
+            int nz = 0;
+            for (int i = 0; i < ColumnCount; i++)
+            {
+                cp[i] = nz;
+                nz += w[i];
+                w[i] = cp[i];
+            }
+            cp[ColumnCount] = nz;
+
+            for (int i = 0; i < RowCount; i++)
+            {
+                for (int p = RowPointers[i]; p < RowPointers[i + 1]; p++)
+                {
+                    int j = w[ColumnIndices[p]]++;
+
+                    // Place A(i,j) as entry C(j,i)
+                    ci[j] = i;
+                    cx[j] = Values[p];
+                }
+            }
+
+            Array.Copy(cx, 0, Values, 0, ValueCount);
+            Buffer.BlockCopy(ci, 0, ColumnIndices, 0, ValueCount * Constants.SizeOfInt);
+            Buffer.BlockCopy(cp, 0, RowPointers, 0, (RowCount + 1) * Constants.SizeOfInt);
+        }
+
         // EXTRACT
 
         public override T[] ToRowMajorArray()
diff --git a/src/UnitTests/LinearAlgebraTests/Double/MatrixTests.cs b/src/UnitTests/LinearAlgebraTests/Double/MatrixTests.cs
index 9bc51296..94b60341 100644
--- a/src/UnitTests/LinearAlgebraTests/Double/MatrixTests.cs
+++ b/src/UnitTests/LinearAlgebraTests/Double/MatrixTests.cs
@@ -27,6 +27,7 @@
 // OTHER DEALINGS IN THE SOFTWARE.
 // </copyright>
 
+using MathNet.Numerics.LinearAlgebra;
 using NUnit.Framework;
 
 namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double
@@ -62,6 +63,54 @@ namespace MathNet.Numerics.UnitTests.LinearAlgebraTests.Double
             }
         }
 
+        /// <summary>
+        /// Can transpose a matrix into a result.
+        /// </summary>
+        /// <param name="name">Matrix name.</param>
+        [TestCase("Singular3x3")]
+        [TestCase("Square3x3")]
+        [TestCase("Square4x4")]
+        [TestCase("Tall3x2")]
+        [TestCase("Wide2x3")]
+        public void CanTransposeMatrixResult(string name)
+        {
+            var matrix = TestMatrices[name];
+            var transpose = Matrix<double>.Build.SameAs(matrix, matrix.ColumnCount, matrix.RowCount);
+            matrix.Transpose(transpose);
+
+            Assert.AreNotSame(matrix, transpose);
+            Assert.AreEqual(matrix.RowCount, transpose.ColumnCount);
+            Assert.AreEqual(matrix.ColumnCount, transpose.RowCount);
+            for (var i = 0; i < matrix.RowCount; i++)
+            {
+                for (var j = 0; j < matrix.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrix[i, j], transpose[j, i]);
+                }
+            }
+        }
+
+        /// <summary>
+        /// Can transpose a square matrix inplace.
+        /// </summary>
+        /// <param name="name">Matrix name.</param>
+        [TestCase("Square4x4")]
+        public void CanTransposeSquareMatrixInplace(string name)
+        {
+            var matrix = TestMatrices[name];
+            var transpose = matrix.Clone();
+            transpose.Transpose(transpose);
+
+            Assert.AreNotSame(matrix, transpose);
+            for (var i = 0; i < matrix.RowCount; i++)
+            {
+                for (var j = 0; j < matrix.ColumnCount; j++)
+                {
+                    Assert.AreEqual(matrix[i, j], transpose[j, i]);
+                }
+            }
+        }
+
         /// <summary>
         /// Can compute Frobenius norm.
         /// </summary>