# C# Hermitian Matrix Example

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```using System;

using CenterSpace.NMath.Core;

namespace CenterSpace.NMath.Examples.CSharp
{
/// <summary>
/// A .NET example in C# demonstrating the features of the Hermitian matrix classes.
/// </summary>
class HermitianMatrixExample
{

static void Main( string[] args )
{
int order = 5;

// Set up a Hermitian matrix S as the conjugate transpose product of a general
// matrix with itself (which is Hermitian).
var rng = new RandGenUniform( -1, 1 );
rng.Reset( 0x124 );
var A = new DoubleComplexMatrix( order, order, rng );

var S = new DoubleHermitianMatrix( NMathFunctions.ConjTransposeProduct( A, A ) );

Console.WriteLine();

Console.WriteLine( "S = " );
Console.WriteLine( S.ToTabDelimited( "F5" ) );

// S =
// (3.12186,0.00000)       (0.12935,0.76321)       (-0.59263,-0.51912)     (1.01693,-0.48541)      (-0.62109,-0.74390)
// (0.12935,-0.76321)      (1.01859,0.00000)       (-0.61581,0.58225)      (0.34714,-1.17980)      (-0.37649,0.35263)
// (-0.59263,0.51912)      (-0.61581,-0.58225)     (2.66911,0.00000)       (-0.78612,2.23106)      (0.09417,0.18527)
// (1.01693,0.48541)       (0.34714,1.17980)       (-0.78612,-2.23106)     (4.10411,0.00000)       (0.59635,0.69605)
// (-0.62109,0.74390)      (-0.37649,-0.35263)     (0.09417,-0.18527)      (0.59635,-0.69605)      (3.97634,0.00000)

// Indexer accessor works just like it does for general matrices.
Console.WriteLine( "S[2,2] = {0}", S[2, 2] );
Console.WriteLine( "S[3,0] = {0}", S[3, 0] );

// You can set the values of elements in a Hermitian matrix using the
// indexer. Note that setting the element in row i and column j to
// a value implicitly sets the element in column j and row i to the
// complex conjugate of that value.
S[2, 1] = new DoubleComplex( 100, -99 );
Console.WriteLine( "S[2,1] = {0}", S[2, 1] ); // (100, -99)
Console.WriteLine( "S[1,2] = {0}", S[1, 2] ); // (100, 99)

// Scalar multiplication and matrix addition/subtraction are supported.
Double a = -.123;
DoubleHermitianMatrix C2 = a * S;
DoubleHermitianMatrix D = C2 + S;
Console.WriteLine();
Console.WriteLine( "D = " );
Console.WriteLine( D.ToTabDelimited( "F5" ) );

// Matrix/vector products too.
var x = new DoubleComplexVector( S.Cols, rng ); // vector of random deviates
DoubleComplexVector y = MatrixFunctions.Product( S, x );
Console.WriteLine( "Sx = {0}", y.ToString( "G3" ) );

// You can also solve linear systems.
DoubleComplexVector x2 = MatrixFunctions.Solve( S, y );

// x and x2 should be about the same. Lets look at the l2 norm of
// their difference.
DoubleComplexVector residual = x - x2;
double residualL2Norm = Math.Sqrt( NMathFunctions.ConjDot( residual, residual ).Real );
Console.WriteLine();
Console.WriteLine( "||x - x2|| = {0}", residualL2Norm );

// You can transform the elements of a Hermitian matrix object by using
// the Transform() method.
C2.DataVector.Transform( NMathFunctions.DoubleComplexCoshFunc );
Console.WriteLine();
Console.WriteLine( "cosh(C2) = " );
Console.WriteLine( C2.ToTabDelimited( "G5" ) );

// For a matrix to satisfy the strict definition of a Hermitian matrix,
// its diagonal elements must be real. The Hermitian matrix classes provide
// a MakeDigaonalReal() method to ensure that your matrix satisfies the
// the strict definition of Hermitian.
C2.MakeDiagonalReal();
Console.WriteLine( "Diagonal element is real: {0}", C2[3, 3].Imag == 0.0 ); // True

// Compute condition number.
double rcond = MatrixFunctions.ConditionNumber( S );
Console.WriteLine();
Console.WriteLine( "Reciprocal condition number = {0}", rcond );

Console.WriteLine();
Console.WriteLine( "Press Enter Key" );
}
}
}

```
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