Jama Class EigenvalueDecomposition

```java.lang.Object
Jama.EigenvalueDecomposition
```
All Implemented Interfaces:
Serializable

`public class EigenvalueDecompositionextends Objectimplements 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().

Serialized Form

Constructor Summary
`EigenvalueDecomposition(Matrix Arg)`
Check for symmetry, then construct the eigenvalue decomposition Structure to access D and V.

Method Summary
` Matrix` `getD()`
Return the block diagonal eigenvalue matrix
` double[]` `getImagEigenvalues()`
Return the imaginary parts of the eigenvalues
` double[]` `getRealEigenvalues()`
Return the real parts of the eigenvalues
` Matrix` `getV()`
Return the eigenvector matrix

Methods inherited from class java.lang.Object
`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

Constructor Detail

EigenvalueDecomposition

`public EigenvalueDecomposition(Matrix Arg)`
Check for symmetry, then construct the eigenvalue decomposition Structure to access D and V.

Parameters:
`Arg` - Square matrix
Method Detail

getV

`public Matrix getV()`
Return the eigenvector matrix

Returns:
V

getRealEigenvalues

`public double[] getRealEigenvalues()`
Return the real parts of the eigenvalues

Returns:
real(diag(D))

getImagEigenvalues

`public double[] getImagEigenvalues()`
Return the imaginary parts of the eigenvalues

Returns:
imag(diag(D))

getD

`public Matrix getD()`
Return the block diagonal eigenvalue matrix

Returns:
D