public class EigenvalueDecomposition extends Object implements Serializable
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().
| Constructor and Description |
|---|
EigenvalueDecomposition(Matrix Arg)
Check for symmetry, then construct the eigenvalue decomposition
Structure to access D and V.
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| Modifier and Type | Method and Description |
|---|---|
Matrix |
getD()
Return the block diagonal eigenvalue matrix
|
double[] |
getImagEigenvalues()
Return the imaginary parts of the eigenvalues
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double[] |
getRealEigenvalues()
Return the real parts of the eigenvalues
|
Matrix |
getV()
Return the eigenvector matrix
|
public EigenvalueDecomposition(Matrix Arg)
Arg - Square matrixpublic Matrix getV()
public double[] getRealEigenvalues()
public double[] getImagEigenvalues()
public Matrix getD()
Jas4pp 1.5 © Java Analysis Studio for Particle Physics