org.biojava.nbio.structure.jama

## Class EigenvalueDecomposition

• All Implemented Interfaces:
Serializable

public class EigenvalueDecomposition
extends Object
implements 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 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