cern.colt.matrix.linalg

## Class EigenvalueDecomposition

• All Implemented Interfaces:
Serializable

```public class EigenvalueDecomposition
extends Object
implements Serializable```
Eigenvalues and eigenvectors of a real matrix A.

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.mult(D.mult(transpose(V))) and V.mult(transpose(V)) 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.mult(V) equals V.mult(D). The matrix V may be badly conditioned, or even singular, so the validity of the equation A = V*D*inverse(V) depends upon Algebra.cond(V).

Serialized Form
• ### Constructor Summary

Constructors
Constructor and Description
`EigenvalueDecomposition(DoubleMatrix2D A)`
Constructs and returns a new eigenvalue decomposition object; The decomposed matrices can be retrieved via instance methods of the returned decomposition object.
• ### Method Summary

Methods
Modifier and Type Method and Description
`DoubleMatrix2D` `getD()`
Returns the block diagonal eigenvalue matrix, D.
`DoubleMatrix1D` `getImagEigenvalues()`
Returns the imaginary parts of the eigenvalues.
`DoubleMatrix1D` `getRealEigenvalues()`
Returns the real parts of the eigenvalues.
`DoubleMatrix2D` `getV()`
Returns the eigenvector matrix, V
`String` `toString()`
Returns a String with (propertyName, propertyValue) pairs.
• ### Methods inherited from class java.lang.Object

`clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait`
• ### Constructor Detail

• #### EigenvalueDecomposition

`public EigenvalueDecomposition(DoubleMatrix2D A)`
Constructs and returns a new eigenvalue decomposition object; The decomposed matrices can be retrieved via instance methods of the returned decomposition object. Checks for symmetry, then constructs the eigenvalue decomposition.
Parameters:
`A` - A square matrix.
Throws:
`IllegalArgumentException` - if A is not square.
• ### Method Detail

• #### getD

`public DoubleMatrix2D getD()`
Returns the block diagonal eigenvalue matrix, D.
Returns:
D
• #### getImagEigenvalues

`public DoubleMatrix1D getImagEigenvalues()`
Returns the imaginary parts of the eigenvalues.
Returns:
imag(diag(D))
• #### getRealEigenvalues

`public DoubleMatrix1D getRealEigenvalues()`
Returns the real parts of the eigenvalues.
Returns:
real(diag(D))
• #### getV

`public DoubleMatrix2D getV()`
Returns the eigenvector matrix, V
Returns:
V
• #### toString

`public String toString()`
Returns a String with (propertyName, propertyValue) pairs. Useful for debugging or to quickly get the rough picture. For example,
```rank          : 3
trace         : 0
```
Overrides:
`toString` in class `Object`