diff --git a/src/Numerics/LinearAlgebra/Builder.cs b/src/Numerics/LinearAlgebra/Builder.cs
index de30b3fa..3cc23640 100644
--- a/src/Numerics/LinearAlgebra/Builder.cs
+++ b/src/Numerics/LinearAlgebra/Builder.cs
@@ -465,7 +465,7 @@ namespace MathNet.Numerics.LinearAlgebra
         public Matrix<T> RandomPositiveDefinite(int order, IContinuousDistribution distribution)
         {
             var a = Random(order, order, distribution);
-            return a.TransposeThisAndMultiply(a);
+            return a.ConjugateTransposeThisAndMultiply(a);
         }
 
         /// <summary>
@@ -475,7 +475,7 @@ namespace MathNet.Numerics.LinearAlgebra
         public Matrix<T> RandomPositiveDefinite(int order)
         {
             var a = Random(order, order, new Normal(MersenneTwister.Default));
-            return a.TransposeThisAndMultiply(a);
+            return a.ConjugateTransposeThisAndMultiply(a);
         }
 
         /// <summary>
@@ -485,7 +485,7 @@ namespace MathNet.Numerics.LinearAlgebra
         public Matrix<T> RandomPositiveDefinite(int order, int seed)
         {
             var a = Random(order, order, new Normal(new MersenneTwister(seed, true)));
-            return a.TransposeThisAndMultiply(a);
+            return a.ConjugateTransposeThisAndMultiply(a);
         }
 
         /// <summary>
diff --git a/src/Numerics/LinearAlgebra/Complex/DenseMatrix.cs b/src/Numerics/LinearAlgebra/Complex/DenseMatrix.cs
index 63ea0f19..0387fd71 100644
--- a/src/Numerics/LinearAlgebra/Complex/DenseMatrix.cs
+++ b/src/Numerics/LinearAlgebra/Complex/DenseMatrix.cs
@@ -727,6 +727,62 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
             base.DoTransposeAndMultiply(other, result);
         }
 
+        /// <summary>
+        /// Multiplies this matrix with the conjugate transpose of another matrix and places the results into the result matrix.
+        /// </summary>
+        /// <param name="other">The matrix to multiply with.</param>
+        /// <param name="result">The result of the multiplication.</param>
+        protected override void DoConjugateTransposeAndMultiply(Matrix<Complex> other, Matrix<Complex> result)
+        {
+            var denseOther = other as DenseMatrix;
+            var denseResult = result as DenseMatrix;
+            if (denseOther != null && denseResult != null)
+            {
+                Control.LinearAlgebraProvider.MatrixMultiplyWithUpdate(
+                    Providers.LinearAlgebra.Transpose.DontTranspose,
+                    Providers.LinearAlgebra.Transpose.ConjugateTranspose,
+                    1.0,
+                    _values,
+                    _rowCount,
+                    _columnCount,
+                    denseOther._values,
+                    denseOther._rowCount,
+                    denseOther._columnCount,
+                    0.0,
+                    denseResult._values);
+                return;
+            }
+
+            var diagonalOther = other.Storage as DiagonalMatrixStorage<Complex>;
+            if (diagonalOther != null)
+            {
+                var diagonal = diagonalOther.Data;
+                var conjugateDiagonal = new Complex[diagonal.Length];
+                for (int i = 0; i < diagonal.Length; i++)
+                {
+                    conjugateDiagonal[i] = diagonal[i].Conjugate();
+                }
+
+                var d = Math.Min(ColumnCount, other.RowCount);
+                if (d < other.RowCount)
+                {
+                    result.ClearSubMatrix(0, RowCount, ColumnCount, other.RowCount - ColumnCount);
+                }
+                int index = 0;
+                for (int j = 0; j < d; j++)
+                {
+                    for (int i = 0; i < RowCount; i++)
+                    {
+                        result.At(i, j, _values[index]*conjugateDiagonal[j]);
+                        index++;
+                    }
+                }
+                return;
+            }
+
+            base.DoConjugateTransposeAndMultiply(other, result);
+        }
+
         /// <summary>
         /// Multiplies the transpose of this matrix with a vector and places the results into the result vector.
         /// </summary>
@@ -736,15 +792,39 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
         {
             var denseRight = rightSide as DenseVector;
             var denseResult = result as DenseVector;
-
-            if (denseRight == null || denseResult == null)
+            if (denseRight != null && denseResult != null)
             {
-                base.DoTransposeThisAndMultiply(rightSide, result);
+                Control.LinearAlgebraProvider.MatrixMultiplyWithUpdate(
+                    Providers.LinearAlgebra.Transpose.Transpose,
+                    Providers.LinearAlgebra.Transpose.DontTranspose,
+                    1.0,
+                    _values,
+                    _rowCount,
+                    _columnCount,
+                    denseRight.Values,
+                    denseRight.Count,
+                    1,
+                    0.0,
+                    denseResult.Values);
+                return;
             }
-            else
+            
+            base.DoTransposeThisAndMultiply(rightSide, result);
+        }
+
+        /// <summary>
+        /// Multiplies the conjugate transpose of this matrix with a vector and places the results into the result vector.
+        /// </summary>
+        /// <param name="rightSide">The vector to multiply with.</param>
+        /// <param name="result">The result of the multiplication.</param>
+        protected override void DoConjugateTransposeThisAndMultiply(Vector<Complex> rightSide, Vector<Complex> result)
+        {
+            var denseRight = rightSide as DenseVector;
+            var denseResult = result as DenseVector;
+            if (denseRight != null && denseResult != null)
             {
                 Control.LinearAlgebraProvider.MatrixMultiplyWithUpdate(
-                    Providers.LinearAlgebra.Transpose.Transpose,
+                    Providers.LinearAlgebra.Transpose.ConjugateTranspose,
                     Providers.LinearAlgebra.Transpose.DontTranspose,
                     1.0,
                     _values,
@@ -755,7 +835,10 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
                     1,
                     0.0,
                     denseResult.Values);
+                return;
             }
+
+            base.DoConjugateTransposeThisAndMultiply(rightSide, result);
         }
 
         /// <summary>
@@ -809,6 +892,57 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
             base.DoTransposeThisAndMultiply(other, result);
         }
 
+        /// <summary>
+        /// Multiplies the transpose of this matrix with another matrix and places the results into the result matrix.
+        /// </summary>
+        /// <param name="other">The matrix to multiply with.</param>
+        /// <param name="result">The result of the multiplication.</param>
+        protected override void DoConjugateTransposeThisAndMultiply(Matrix<Complex> other, Matrix<Complex> result)
+        {
+            var denseOther = other as DenseMatrix;
+            var denseResult = result as DenseMatrix;
+            if (denseOther != null && denseResult != null)
+            {
+                Control.LinearAlgebraProvider.MatrixMultiplyWithUpdate(
+                    Providers.LinearAlgebra.Transpose.ConjugateTranspose,
+                    Providers.LinearAlgebra.Transpose.DontTranspose,
+                    1.0,
+                    _values,
+                    _rowCount,
+                    _columnCount,
+                    denseOther._values,
+                    denseOther._rowCount,
+                    denseOther._columnCount,
+                    0.0,
+                    denseResult._values);
+                return;
+            }
+
+            var diagonalOther = other.Storage as DiagonalMatrixStorage<Complex>;
+            if (diagonalOther != null)
+            {
+                var diagonal = diagonalOther.Data;
+                var d = Math.Min(RowCount, other.ColumnCount);
+                if (d < other.ColumnCount)
+                {
+                    result.ClearSubMatrix(0, ColumnCount, RowCount, other.ColumnCount - RowCount);
+                }
+                int index = 0;
+                for (int i = 0; i < ColumnCount; i++)
+                {
+                    for (int j = 0; j < d; j++)
+                    {
+                        result.At(i, j, _values[index].Conjugate()*diagonal[j]);
+                        index++;
+                    }
+                    index += (RowCount - d);
+                }
+                return;
+            }
+
+            base.DoConjugateTransposeThisAndMultiply(other, result);
+        }
+
         /// <summary>
         /// Negate each element of this matrix and place the results into the result matrix.
         /// </summary>
diff --git a/src/Numerics/LinearAlgebra/Complex/Matrix.cs b/src/Numerics/LinearAlgebra/Complex/Matrix.cs
index 771391fb..d2ec6f96 100644
--- a/src/Numerics/LinearAlgebra/Complex/Matrix.cs
+++ b/src/Numerics/LinearAlgebra/Complex/Matrix.cs
@@ -293,6 +293,27 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
             }
         }
 
+        /// <summary>
+        /// Multiplies this matrix with the conjugate transpose of another matrix and places the results into the result matrix.
+        /// </summary>
+        /// <param name="other">The matrix to multiply with.</param>
+        /// <param name="result">The result of the multiplication.</param>
+        protected override void DoConjugateTransposeAndMultiply(Matrix<Complex> other, Matrix<Complex> result)
+        {
+            for (var j = 0; j < other.RowCount; j++)
+            {
+                for (var i = 0; i < RowCount; i++)
+                {
+                    var s = Complex.Zero;
+                    for (var l = 0; l < ColumnCount; l++)
+                    {
+                        s += At(i, l)*other.At(j, l).Conjugate();
+                    }
+                    result.At(i, j, s);
+                }
+            }
+        }
+
         /// <summary>
         /// Multiplies the transpose of this matrix with another matrix and places the results into the result matrix.
         /// </summary>
@@ -314,6 +335,27 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
             }
         }
 
+        /// <summary>
+        /// Multiplies the transpose of this matrix with another matrix and places the results into the result matrix.
+        /// </summary>
+        /// <param name="other">The matrix to multiply with.</param>
+        /// <param name="result">The result of the multiplication.</param>
+        protected override void DoConjugateTransposeThisAndMultiply(Matrix<Complex> other, Matrix<Complex> result)
+        {
+            for (var j = 0; j < other.ColumnCount; j++)
+            {
+                for (var i = 0; i < ColumnCount; i++)
+                {
+                    var s = Complex.Zero;
+                    for (var l = 0; l < RowCount; l++)
+                    {
+                        s += At(l, i).Conjugate()*other.At(l, j);
+                    }
+                    result.At(i, j, s);
+                }
+            }
+        }
+
         /// <summary>
         /// Multiplies the transpose of this matrix with a vector and places the results into the result vector.
         /// </summary>
@@ -332,6 +374,24 @@ namespace MathNet.Numerics.LinearAlgebra.Complex
             }
         }
 
+        /// <summary>
+        /// Multiplies the conjugate transpose of this matrix with a vector and places the results into the result vector.
+        /// </summary>
+        /// <param name="rightSide">The vector to multiply with.</param>
+        /// <param name="result">The result of the multiplication.</param>
+        protected override void DoConjugateTransposeThisAndMultiply(Vector<Complex> rightSide, Vector<Complex> result)
+        {
+            for (var i = 0; i < ColumnCount; i++)
+            {
+                var s = Complex.Zero;
+                for (var j = 0; j < RowCount; j++)
+                {
+                    s += At(j, i).Conjugate()*rightSide[j];
+                }
+                result[i] = s;
+            }
+        }
+
         /// <summary>
         /// Negate each element of this matrix and place the results into the result matrix.
         /// </summary>
diff --git a/src/Numerics/LinearAlgebra/Complex32/DenseMatrix.cs b/src/Numerics/LinearAlgebra/Complex32/DenseMatrix.cs
index cfe659f0..443c0883 100644
--- a/src/Numerics/LinearAlgebra/Complex32/DenseMatrix.cs
+++ b/src/Numerics/LinearAlgebra/Complex32/DenseMatrix.cs
@@ -722,6 +722,62 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
             base.DoTransposeAndMultiply(other, result);
         }
 
+        /// <summary>
+        /// Multiplies this matrix with the conjugate transpose of another matrix and places the results into the result matrix.
+        /// </summary>
+        /// <param name="other">The matrix to multiply with.</param>
+        /// <param name="result">The result of the multiplication.</param>
+        protected override void DoConjugateTransposeAndMultiply(Matrix<Complex32> other, Matrix<Complex32> result)
+        {
+            var denseOther = other as DenseMatrix;
+            var denseResult = result as DenseMatrix;
+            if (denseOther != null && denseResult != null)
+            {
+                Control.LinearAlgebraProvider.MatrixMultiplyWithUpdate(
+                    Providers.LinearAlgebra.Transpose.DontTranspose,
+                    Providers.LinearAlgebra.Transpose.ConjugateTranspose,
+                    1.0f,
+                    _values,
+                    _rowCount,
+                    _columnCount,
+                    denseOther._values,
+                    denseOther._rowCount,
+                    denseOther._columnCount,
+                    0.0f,
+                    denseResult._values);
+                return;
+            }
+
+            var diagonalOther = other.Storage as DiagonalMatrixStorage<Complex32>;
+            if (diagonalOther != null)
+            {
+                var diagonal = diagonalOther.Data;
+                var conjugateDiagonal = new Complex32[diagonal.Length];
+                for (int i = 0; i < diagonal.Length; i++)
+                {
+                    conjugateDiagonal[i] = diagonal[i].Conjugate();
+                }
+
+                var d = Math.Min(ColumnCount, other.RowCount);
+                if (d < other.RowCount)
+                {
+                    result.ClearSubMatrix(0, RowCount, ColumnCount, other.RowCount - ColumnCount);
+                }
+                int index = 0;
+                for (int j = 0; j < d; j++)
+                {
+                    for (int i = 0; i < RowCount; i++)
+                    {
+                        result.At(i, j, _values[index]*conjugateDiagonal[j]);
+                        index++;
+                    }
+                }
+                return;
+            }
+
+            base.DoConjugateTransposeAndMultiply(other, result);
+        }
+
         /// <summary>
         /// Multiplies the transpose of this matrix with a vector and places the results into the result vector.
         /// </summary>
@@ -753,6 +809,35 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
             }
         }
 
+        /// <summary>
+        /// Multiplies the conjugate transpose of this matrix with a vector and places the results into the result vector.
+        /// </summary>
+        /// <param name="rightSide">The vector to multiply with.</param>
+        /// <param name="result">The result of the multiplication.</param>
+        protected override void DoConjugateTransposeThisAndMultiply(Vector<Complex32> rightSide, Vector<Complex32> result)
+        {
+            var denseRight = rightSide as DenseVector;
+            var denseResult = result as DenseVector;
+            if (denseRight != null && denseResult != null)
+            {
+                Control.LinearAlgebraProvider.MatrixMultiplyWithUpdate(
+                    Providers.LinearAlgebra.Transpose.ConjugateTranspose,
+                    Providers.LinearAlgebra.Transpose.DontTranspose,
+                    1.0f,
+                    _values,
+                    _rowCount,
+                    _columnCount,
+                    denseRight.Values,
+                    denseRight.Count,
+                    1,
+                    0.0f,
+                    denseResult.Values);
+                return;
+            }
+
+            base.DoConjugateTransposeThisAndMultiply(rightSide, result);
+        }
+
         /// <summary>
         /// Multiplies the transpose of this matrix with another matrix and places the results into the result matrix.
         /// </summary>
@@ -804,6 +889,57 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
             base.DoTransposeThisAndMultiply(other, result);
         }
 
+        /// <summary>
+        /// Multiplies the transpose of this matrix with another matrix and places the results into the result matrix.
+        /// </summary>
+        /// <param name="other">The matrix to multiply with.</param>
+        /// <param name="result">The result of the multiplication.</param>
+        protected override void DoConjugateTransposeThisAndMultiply(Matrix<Complex32> other, Matrix<Complex32> result)
+        {
+            var denseOther = other as DenseMatrix;
+            var denseResult = result as DenseMatrix;
+            if (denseOther != null && denseResult != null)
+            {
+                Control.LinearAlgebraProvider.MatrixMultiplyWithUpdate(
+                    Providers.LinearAlgebra.Transpose.ConjugateTranspose,
+                    Providers.LinearAlgebra.Transpose.DontTranspose,
+                    1.0f,
+                    _values,
+                    _rowCount,
+                    _columnCount,
+                    denseOther._values,
+                    denseOther._rowCount,
+                    denseOther._columnCount,
+                    0.0f,
+                    denseResult._values);
+                return;
+            }
+
+            var diagonalOther = other.Storage as DiagonalMatrixStorage<Complex32>;
+            if (diagonalOther != null)
+            {
+                var diagonal = diagonalOther.Data;
+                var d = Math.Min(RowCount, other.ColumnCount);
+                if (d < other.ColumnCount)
+                {
+                    result.ClearSubMatrix(0, ColumnCount, RowCount, other.ColumnCount - RowCount);
+                }
+                int index = 0;
+                for (int i = 0; i < ColumnCount; i++)
+                {
+                    for (int j = 0; j < d; j++)
+                    {
+                        result.At(i, j, _values[index].Conjugate()*diagonal[j]);
+                        index++;
+                    }
+                    index += (RowCount - d);
+                }
+                return;
+            }
+
+            base.DoConjugateTransposeThisAndMultiply(other, result);
+        }
+
         /// <summary>
         /// Negate each element of this matrix and place the results into the result matrix.
         /// </summary>
diff --git a/src/Numerics/LinearAlgebra/Complex32/Matrix.cs b/src/Numerics/LinearAlgebra/Complex32/Matrix.cs
index b9f248d2..abcf6d44 100644
--- a/src/Numerics/LinearAlgebra/Complex32/Matrix.cs
+++ b/src/Numerics/LinearAlgebra/Complex32/Matrix.cs
@@ -287,6 +287,27 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
             }
         }
 
+        /// <summary>
+        /// Multiplies this matrix with the conjugate transpose of another matrix and places the results into the result matrix.
+        /// </summary>
+        /// <param name="other">The matrix to multiply with.</param>
+        /// <param name="result">The result of the multiplication.</param>
+        protected override void DoConjugateTransposeAndMultiply(Matrix<Complex32> other, Matrix<Complex32> result)
+        {
+            for (var j = 0; j < other.RowCount; j++)
+            {
+                for (var i = 0; i < RowCount; i++)
+                {
+                    var s = Complex32.Zero;
+                    for (var l = 0; l < ColumnCount; l++)
+                    {
+                        s += At(i, l)*other.At(j, l).Conjugate();
+                    }
+                    result.At(i, j, s);
+                }
+            }
+        }
+
         /// <summary>
         /// Multiplies the transpose of this matrix with another matrix and places the results into the result matrix.
         /// </summary>
@@ -308,6 +329,27 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
             }
         }
 
+        /// <summary>
+        /// Multiplies the transpose of this matrix with another matrix and places the results into the result matrix.
+        /// </summary>
+        /// <param name="other">The matrix to multiply with.</param>
+        /// <param name="result">The result of the multiplication.</param>
+        protected override void DoConjugateTransposeThisAndMultiply(Matrix<Complex32> other, Matrix<Complex32> result)
+        {
+            for (var j = 0; j < other.ColumnCount; j++)
+            {
+                for (var i = 0; i < ColumnCount; i++)
+                {
+                    var s = Complex32.Zero;
+                    for (var l = 0; l < RowCount; l++)
+                    {
+                        s += At(l, i).Conjugate()*other.At(l, j);
+                    }
+                    result.At(i, j, s);
+                }
+            }
+        }
+
         /// <summary>
         /// Multiplies the transpose of this matrix with a vector and places the results into the result vector.
         /// </summary>
@@ -326,6 +368,24 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32
             }
         }
 
+        /// <summary>
+        /// Multiplies the conjugate transpose of this matrix with a vector and places the results into the result vector.
+        /// </summary>
+        /// <param name="rightSide">The vector to multiply with.</param>
+        /// <param name="result">The result of the multiplication.</param>
+        protected override void DoConjugateTransposeThisAndMultiply(Vector<Complex32> rightSide, Vector<Complex32> result)
+        {
+            for (var i = 0; i < ColumnCount; i++)
+            {
+                var s = Complex32.Zero;
+                for (var j = 0; j < RowCount; j++)
+                {
+                    s += At(j, i).Conjugate()*rightSide[j];
+                }
+                result[i] = s;
+            }
+        }
+
         /// <summary>
         /// Negate each element of this matrix and place the results into the result matrix.
         /// </summary>
diff --git a/src/Numerics/LinearAlgebra/Double/Matrix.cs b/src/Numerics/LinearAlgebra/Double/Matrix.cs
index b70d67f7..a2ff1428 100644
--- a/src/Numerics/LinearAlgebra/Double/Matrix.cs
+++ b/src/Numerics/LinearAlgebra/Double/Matrix.cs
@@ -277,6 +277,16 @@ namespace MathNet.Numerics.LinearAlgebra.Double
             }
         }
 
+        /// <summary>
+        /// Multiplies this matrix with the conjugate transpose of another matrix and places the results into the result matrix.
+        /// </summary>
+        /// <param name="other">The matrix to multiply with.</param>
+        /// <param name="result">The result of the multiplication.</param>
+        protected override sealed void DoConjugateTransposeAndMultiply(Matrix<double> other, Matrix<double> result)
+        {
+            DoTransposeAndMultiply(other, result);
+        }
+
         /// <summary>
         /// Multiplies the transpose of this matrix with another matrix and places the results into the result matrix.
         /// </summary>
@@ -298,6 +308,16 @@ namespace MathNet.Numerics.LinearAlgebra.Double
             }
         }
 
+        /// <summary>
+        /// Multiplies the transpose of this matrix with another matrix and places the results into the result matrix.
+        /// </summary>
+        /// <param name="other">The matrix to multiply with.</param>
+        /// <param name="result">The result of the multiplication.</param>
+        protected override sealed void DoConjugateTransposeThisAndMultiply(Matrix<double> other, Matrix<double> result)
+        {
+            DoTransposeThisAndMultiply(other, result);
+        }
+
         /// <summary>
         /// Multiplies the transpose of this matrix with a vector and places the results into the result vector.
         /// </summary>
@@ -316,6 +336,16 @@ namespace MathNet.Numerics.LinearAlgebra.Double
             }
         }
 
+        /// <summary>
+        /// Multiplies the conjugate transpose of this matrix with a vector and places the results into the result vector.
+        /// </summary>
+        /// <param name="rightSide">The vector to multiply with.</param>
+        /// <param name="result">The result of the multiplication.</param>
+        protected override void DoConjugateTransposeThisAndMultiply(Vector<double> rightSide, Vector<double> result)
+        {
+            DoTransposeThisAndMultiply(rightSide, result);
+        }
+
         /// <summary>
         /// Negate each element of this matrix and place the results into the result matrix.
         /// </summary>
diff --git a/src/Numerics/LinearAlgebra/Matrix.Arithmetic.cs b/src/Numerics/LinearAlgebra/Matrix.Arithmetic.cs
index b6e3b44d..1d778495 100644
--- a/src/Numerics/LinearAlgebra/Matrix.Arithmetic.cs
+++ b/src/Numerics/LinearAlgebra/Matrix.Arithmetic.cs
@@ -122,12 +122,19 @@ namespace MathNet.Numerics.LinearAlgebra
         protected abstract void DoMultiply(Matrix<T> other, Matrix<T> result);
 
         /// <summary>
-        /// Multiplies this matrix with transpose of another matrix and places the results into the result matrix.
+        /// Multiplies this matrix with the transpose of another matrix and places the results into the result matrix.
         /// </summary>
         /// <param name="other">The matrix to multiply with.</param>
         /// <param name="result">The result of the multiplication.</param>
         protected abstract void DoTransposeAndMultiply(Matrix<T> other, Matrix<T> result);
 
+        /// <summary>
+        /// Multiplies this matrix with the conjugate transpose of another matrix and places the results into the result matrix.
+        /// </summary>
+        /// <param name="other">The matrix to multiply with.</param>
+        /// <param name="result">The result of the multiplication.</param>
+        protected abstract void DoConjugateTransposeAndMultiply(Matrix<T> other, Matrix<T> result);
+
         /// <summary>
         /// Multiplies the transpose of this matrix with a vector and places the results into the result vector.
         /// </summary>
@@ -135,6 +142,13 @@ namespace MathNet.Numerics.LinearAlgebra
         /// <param name="result">The result of the multiplication.</param>
         protected abstract void DoTransposeThisAndMultiply(Vector<T> rightSide, Vector<T> result);
 
+        /// <summary>
+        /// Multiplies the conjugate transpose of this matrix with a vector and places the results into the result vector.
+        /// </summary>
+        /// <param name="rightSide">The vector to multiply with.</param>
+        /// <param name="result">The result of the multiplication.</param>
+        protected abstract void DoConjugateTransposeThisAndMultiply(Vector<T> rightSide, Vector<T> result);
+
         /// <summary>
         /// Multiplies the transpose of this matrix with another matrix and places the results into the result matrix.
         /// </summary>
@@ -142,6 +156,13 @@ namespace MathNet.Numerics.LinearAlgebra
         /// <param name="result">The result of the multiplication.</param>
         protected abstract void DoTransposeThisAndMultiply(Matrix<T> other, Matrix<T> result);
 
+        /// <summary>
+        /// Multiplies the transpose of this matrix with another matrix and places the results into the result matrix.
+        /// </summary>
+        /// <param name="other">The matrix to multiply with.</param>
+        /// <param name="result">The result of the multiplication.</param>
+        protected abstract void DoConjugateTransposeThisAndMultiply(Matrix<T> other, Matrix<T> result);
+
         /// <summary>
         /// Divides each element of the matrix by a scalar and places results into the result matrix.
         /// </summary>
@@ -807,6 +828,145 @@ namespace MathNet.Numerics.LinearAlgebra
             return result;
         }
 
+
+
+        /// <summary>
+        /// Multiplies this matrix with the conjugate transpose of another matrix and places the results into the result matrix.
+        /// </summary>
+        /// <param name="other">The matrix to multiply with.</param>
+        /// <param name="result">The result of the multiplication.</param>
+        /// <exception cref="ArgumentException">If <strong>this.Columns != other.ColumnCount</strong>.</exception>
+        /// <exception cref="ArgumentException">If the result matrix's dimensions are not the this.RowCount x other.RowCount.</exception>
+        public virtual void ConjugateTransposeAndMultiply(Matrix<T> other, Matrix<T> result)
+        {
+            if (ColumnCount != other.ColumnCount || result.RowCount != RowCount || result.ColumnCount != other.RowCount)
+            {
+                throw DimensionsDontMatch<ArgumentException>(this, other, result);
+            }
+
+            if (ReferenceEquals(this, result) || ReferenceEquals(other, result))
+            {
+                var tmp = Build.SameAs(result);
+                DoConjugateTransposeAndMultiply(other, tmp);
+                tmp.CopyTo(result);
+            }
+            else
+            {
+                DoConjugateTransposeAndMultiply(other, result);
+            }
+        }
+
+        /// <summary>
+        /// Multiplies this matrix with the conjugate transpose of another matrix and returns the result.
+        /// </summary>
+        /// <param name="other">The matrix to multiply with.</param>
+        /// <exception cref="ArgumentException">If <strong>this.Columns != other.ColumnCount</strong>.</exception>
+        /// <returns>The result of the multiplication.</returns>
+        public Matrix<T> ConjugateTransposeAndMultiply(Matrix<T> other)
+        {
+            if (ColumnCount != other.ColumnCount)
+            {
+                throw DimensionsDontMatch<ArgumentException>(this, other);
+            }
+
+            var result = Build.SameAs(this, other, RowCount, other.RowCount);
+            DoConjugateTransposeAndMultiply(other, result);
+            return result;
+        }
+
+        /// <summary>
+        /// Multiplies the conjugate transpose of this matrix by a vector and returns the result.
+        /// </summary>
+        /// <param name="rightSide">The vector to multiply with.</param>
+        /// <returns>The result of the multiplication.</returns>
+        /// <exception cref="ArgumentException">If <c>this.RowCount != rightSide.Count</c>.</exception>
+        public Vector<T> ConjugateTransposeThisAndMultiply(Vector<T> rightSide)
+        {
+            if (RowCount != rightSide.Count)
+            {
+                throw DimensionsDontMatch<ArgumentException>(this, rightSide, "rightSide");
+            }
+
+            var result = Vector<T>.Build.SameAs(this, rightSide, ColumnCount);
+            DoConjugateTransposeThisAndMultiply(rightSide, result);
+            return result;
+        }
+
+        /// <summary>
+        /// Multiplies the conjugate transpose of this matrix with a vector and places the results into the result vector.
+        /// </summary>
+        /// <param name="rightSide">The vector to multiply with.</param>
+        /// <param name="result">The result of the multiplication.</param>
+        /// <exception cref="ArgumentException">If <strong>result.Count != this.ColumnCount</strong>.</exception>
+        /// <exception cref="ArgumentException">If <strong>this.RowCount != <paramref name="rightSide"/>.Count</strong>.</exception>
+        public void ConjugateTransposeThisAndMultiply(Vector<T> rightSide, Vector<T> result)
+        {
+            if (RowCount != rightSide.Count)
+            {
+                throw DimensionsDontMatch<ArgumentException>(this, rightSide, "rightSide");
+            }
+
+            if (ColumnCount != result.Count)
+            {
+                throw DimensionsDontMatch<ArgumentException>(this, result, "result");
+            }
+
+            if (ReferenceEquals(rightSide, result))
+            {
+                var tmp = Vector<T>.Build.SameAs(result);
+                DoConjugateTransposeThisAndMultiply(rightSide, tmp);
+                tmp.CopyTo(result);
+            }
+            else
+            {
+                DoConjugateTransposeThisAndMultiply(rightSide, result);
+            }
+        }
+
+        /// <summary>
+        /// Multiplies the conjugate transpose of this matrix with another matrix and places the results into the result matrix.
+        /// </summary>
+        /// <param name="other">The matrix to multiply with.</param>
+        /// <param name="result">The result of the multiplication.</param>
+        /// <exception cref="ArgumentException">If <strong>this.Rows != other.RowCount</strong>.</exception>
+        /// <exception cref="ArgumentException">If the result matrix's dimensions are not the this.ColumnCount x other.ColumnCount.</exception>
+        public void ConjugateTransposeThisAndMultiply(Matrix<T> other, Matrix<T> result)
+        {
+            if (RowCount != other.RowCount || result.RowCount != ColumnCount || result.ColumnCount != other.ColumnCount)
+            {
+                throw DimensionsDontMatch<ArgumentException>(this, other, result);
+            }
+
+            if (ReferenceEquals(this, result) || ReferenceEquals(other, result))
+            {
+                var tmp = Build.SameAs(result);
+                DoConjugateTransposeThisAndMultiply(other, tmp);
+                tmp.CopyTo(result);
+            }
+            else
+            {
+                DoConjugateTransposeThisAndMultiply(other, result);
+            }
+        }
+
+        /// <summary>
+        /// Multiplies the conjugate transpose of this matrix with another matrix and returns the result.
+        /// </summary>
+        /// <param name="other">The matrix to multiply with.</param>
+        /// <exception cref="ArgumentException">If <strong>this.Rows != other.RowCount</strong>.</exception>
+        /// <returns>The result of the multiplication.</returns>
+        public Matrix<T> ConjugateTransposeThisAndMultiply(Matrix<T> other)
+        {
+            if (RowCount != other.RowCount)
+            {
+                throw DimensionsDontMatch<ArgumentException>(this, other);
+            }
+
+            var result = Build.SameAs(this, other, ColumnCount, other.ColumnCount);
+            DoConjugateTransposeThisAndMultiply(other, result);
+            return result;
+        }
+
         /// <summary>
         /// Negate each element of this matrix.
         /// </summary>
diff --git a/src/Numerics/LinearAlgebra/Single/Matrix.cs b/src/Numerics/LinearAlgebra/Single/Matrix.cs
index b8737c0e..a13fda54 100644
--- a/src/Numerics/LinearAlgebra/Single/Matrix.cs
+++ b/src/Numerics/LinearAlgebra/Single/Matrix.cs
@@ -277,6 +277,16 @@ namespace MathNet.Numerics.LinearAlgebra.Single
             }
         }
 
+        /// <summary>
+        /// Multiplies this matrix with the conjugate transpose of another matrix and places the results into the result matrix.
+        /// </summary>
+        /// <param name="other">The matrix to multiply with.</param>
+        /// <param name="result">The result of the multiplication.</param>
+        protected override sealed void DoConjugateTransposeAndMultiply(Matrix<float> other, Matrix<float> result)
+        {
+            DoTransposeAndMultiply(other, result);
+        }
+
         /// <summary>
         /// Multiplies the transpose of this matrix with another matrix and places the results into the result matrix.
         /// </summary>
@@ -298,6 +308,16 @@ namespace MathNet.Numerics.LinearAlgebra.Single
             }
         }
 
+        /// <summary>
+        /// Multiplies the transpose of this matrix with another matrix and places the results into the result matrix.
+        /// </summary>
+        /// <param name="other">The matrix to multiply with.</param>
+        /// <param name="result">The result of the multiplication.</param>
+        protected override sealed void DoConjugateTransposeThisAndMultiply(Matrix<float> other, Matrix<float> result)
+        {
+            DoTransposeThisAndMultiply(other, result);
+        }
+
         /// <summary>
         /// Multiplies the transpose of this matrix with a vector and places the results into the result vector.
         /// </summary>
@@ -316,6 +336,16 @@ namespace MathNet.Numerics.LinearAlgebra.Single
             }
         }
 
+        /// <summary>
+        /// Multiplies the conjugate transpose of this matrix with a vector and places the results into the result vector.
+        /// </summary>
+        /// <param name="rightSide">The vector to multiply with.</param>
+        /// <param name="result">The result of the multiplication.</param>
+        protected override void DoConjugateTransposeThisAndMultiply(Vector<float> rightSide, Vector<float> result)
+        {
+            DoTransposeThisAndMultiply(rightSide, result);
+        }
+
         /// <summary>
         /// Computes the modulus for each element of the matrix.
         /// </summary>