EigenvalueDecomposition
Keywords: Jama.EigenvalueDecomposition class

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## Jama
Class EigenvalueDecomposition

    java.lang.Object
      Jama.EigenvalueDecomposition

All Implemented Interfaces:
  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().

See Also:
  Serialized Form

Constructor Summary
`EigenvalueDecomposition(Matrix Arg)` Check for symmetry, then construct the eigenvalue decomposition

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

  Parameters:
    `A` - 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

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