Jama
Class EigenvalueDecomposition
java.lang.Object
Jama.EigenvalueDecomposition
- java.io.Serializable
public class EigenvalueDecomposition
extends java.lang.Object
implements java.io.Serializable
Eigenvalues and eigenvectors of a real matrix.
If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is
diagonal and the eigenvector matrix V is orthogonal.
I.e. A = V.times(D.times(V.transpose())) and
V.times(V.transpose()) equals the identity matrix.
If A is not symmetric, then 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,
i.e. A.times(V) equals V.times(D). The matrix V may be badly
conditioned, or even singular, so the validity of the equation
A = V*D*inverse(V) depends upon V.cond().
EigenvalueDecomposition
public EigenvalueDecomposition(Matrix Arg)
Check for symmetry, then construct the eigenvalue decomposition
getD
public Matrix getD()
Return the block diagonal eigenvalue matrix
getImagEigenvalues
public double[] getImagEigenvalues()
Return the imaginary parts of the eigenvalues
getRealEigenvalues
public double[] getRealEigenvalues()
Return the real parts of the eigenvalues
getV
public Matrix getV()
Return the eigenvector matrix