ComplexMatrixConjugateTranspose Method

Returns the conjugate transpose of this instance.

Definition

Namespace: Novacta.Analytics
Assembly: Novacta.Analytics (in Novacta.Analytics.dll) Version: 2.1.0+428f3840cfab98dda567bb0ed350b302533e273a
C#
public ComplexMatrix ConjugateTranspose()

Return Value

ComplexMatrix
The conjugate transpose of this instance.

Remarks

Let LaTeX equation and LaTeX equation be the number of rows and columns, respectively, of this instance, and consider its generic entry

LaTeX equation

The method returns the conjugate transpose of this instance, i.e. a matrix, say LaTeX equation, having LaTeX equation rows and LaTeX equation columns, whose generic entry is:

LaTeX equation

where LaTeX equation is the conjugate of complex LaTeX equation.

Example

In the following example, the conjugate transpose of a matrix is computed.

C#
using System;
using System.Numerics;

namespace Novacta.Analytics.CodeExamples
{
    public class ComplexOutPlaceConjugateTransposeExample0  
    {
        public void Main()
        {
            // Create a matrix.
            var data = new Complex[6] {
                new(1, -1), new(5, -5),
                new(2, -2), new(6, -6),
                new(3, -3), new(7, -7)
            };
            var matrix = ComplexMatrix.Dense(3, 2, data, StorageOrder.RowMajor);
            Console.WriteLine("The data matrix:");
            Console.WriteLine(matrix);

            // Return its conjugate transpose.
            var transposedMatrix = matrix.ConjugateTranspose();

            Console.WriteLine();
            Console.WriteLine("Matrix conjugate transpose:");
            Console.WriteLine(transposedMatrix);

            // Compute the conjugate transpose using a read-only wrapper
            // of the data matrix.
            ReadOnlyComplexMatrix readOnlyMatrix = matrix.AsReadOnly();
            var transposedReadOnlyMatrix = readOnlyMatrix.ConjugateTranspose();

            Console.WriteLine();
            Console.WriteLine("Read only matrix transpose:");
            Console.WriteLine(transposedReadOnlyMatrix);
        }
    }
}

// Executing method Main() produces the following output:
// 
// The data matrix:
// (                1,               -1) (                5,               -5) 
// (                2,               -2) (                6,               -6) 
// (                3,               -3) (                7,               -7) 
// 
// 
// 
// Matrix conjugate transpose:
// (                1,                1) (                2,                2) (                3,                3) 
// (                5,                5) (                6,                6) (                7,                7) 
// 
// 
// 
// Read only matrix transpose:
// (                1,                1) (                2,                2) (                3,                3) 
// (                5,                5) (                6,                6) (                7,                7) 
// 
//

See Also