IEigenvalue |
Determines the eigenvalues and eigenvectors of a real square matrix.
Namespace: Altaxo.Calc.LinearAlgebra
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
SyntaxC#
public interface IEigenvalueDecomposition
The IEigenvalueDecomposition type exposes the following members.
Properties| Name | Description | |
|---|---|---|
 | DiagonalMatrix | Returns the block diagonal eigenvalue matrix. |
| EigenvectorMatrix | Returns the eigenvector matrix. |
| ImaginaryEigenvalues | Returns the imaginary parts of the eigenvalues. |
| RealEigenvalues | Returns the real parts of the eigenvalues. |
Remarks
If A is symmetric, then A = V * D * V' and A = V * V'
where the eigenvalue matrix D is diagonal and the eigenvector matrix V is orthogonal.
If A is not symmetric, the eigenvalue matrix D is block diagonal
with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues,
lambda+i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda].
The columns of V represent the eigenvectors in the sense that A * V = V * D.
The matrix V may be badly conditioned, or even singular, so the validity of the equation
A=V*D*inverse(V) depends upon the condition of V.
See Also