org.apache.mahout.math.solver

## Class EigenDecomposition

• ```public class EigenDecomposition
extends Object```
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().

• ### Constructor Summary

Constructors
Constructor and Description
`EigenDecomposition(Matrix x)`
```EigenDecomposition(Matrix x, boolean isSymmetric)```
• ### Method Summary

Methods
Modifier and Type Method and Description
`Matrix` `getD()`
Return the block diagonal eigenvalue matrix
`Vector` `getImagEigenvalues()`
Return the imaginary parts of the eigenvalues
`Vector` `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

• #### EigenDecomposition

`public EigenDecomposition(Matrix x)`
• #### EigenDecomposition

```public EigenDecomposition(Matrix x,
boolean isSymmetric)```
• ### Method Detail

• #### getV

`public Matrix getV()`
Return the eigenvector matrix
Returns:
V
• #### getRealEigenvalues

`public Vector getRealEigenvalues()`
Return the real parts of the eigenvalues
• #### getImagEigenvalues

`public Vector getImagEigenvalues()`
Return the imaginary parts of the eigenvalues
• #### getD

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