SpectralDecomposition Class

public static class SpectralDecomposition

Public NotInheritable Class SpectralDecomposition

public ref class SpectralDecomposition abstract sealed

[<AbstractClassAttribute>]
[<SealedAttribute>]
type SpectralDecomposition = class end

Inheritance

Object    SpectralDecomposition

Let be a normal matrix, i.e., it satisfies



where returns the conjugate transpose of .

The Spectral Decomposition of is a factorization having the following form:



where is a orthonormal matrix whose columns are eigenvectors of , and is a diagonal matrix, whose main diagonal entries correspond to the eigenvalues of .

Method Decompose(ComplexMatrix, Boolean, ComplexMatrix) returns matrices and when is a Hermitian complex matrix, while Decompose(DoubleMatrix, Boolean, DoubleMatrix) returns the same matrices for a symmetric real matrix.

Method GetEigenvalues(DoubleMatrix, Boolean) and its overloads return the eigenvalues involved in a spectral decomposition, without computing the corresponding eigenvectors.

Reference

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