 | SpectralDecomposition Class |
Inheritance HierarchyNamespace: Novacta.Analytics.Advanced
Assembly: Novacta.Analytics (in Novacta.Analytics.dll) Version: 2.0.0
SyntaxMethods| Name | Description | |
|---|---|---|
  | Decompose(ComplexMatrix, Boolean, ComplexMatrix) |
Computes eigenvalues and eigenvectors of the
specified Hermitian complex matrix.
|
 | Decompose(DoubleMatrix, Boolean, DoubleMatrix) |
Computes eigenvalues and eigenvectors of the
specified symmetric real matrix.
|
| Decompose(ReadOnlyComplexMatrix, Boolean, ComplexMatrix) |
Computes eigenvalues and eigenvectors of the
specified Hermitian complex matrix.
|
| Decompose(ReadOnlyDoubleMatrix, Boolean, DoubleMatrix) |
Computes eigenvalues and eigenvectors of the
specified symmetric real matrix.
|
| GetEigenvalues(ComplexMatrix, Boolean) |
Computes the eigenvalues of the
specified Hermitian complex matrix.
|
| GetEigenvalues(DoubleMatrix, Boolean) |
Computes the eigenvalues of the specified symmetric real matrix.
|
| GetEigenvalues(ReadOnlyComplexMatrix, Boolean) |
Computes the eigenvalues of the
specified Hermitian complex matrix.
|
| GetEigenvalues(ReadOnlyDoubleMatrix, Boolean) |
Computes the eigenvalues of the specified symmetric real matrix.
|
Remarks
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.
See Also