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java.lang.Object org.jmatrices.dbl.decomposition.EigenvalueDecomposition
EigenvalueDecomposition
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().
The code is basically JAMA code with modifications made to fit in the scheme of things.
Author: purangp
Date: 13.03.2004 Time: 14:25:02
Constructor Summary | |
EigenvalueDecomposition(Matrix matrix)
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 todo a way to test eigen values is -> sum of eigenvalues = getTrace of the matrix and product of eigenvalues = detrminant of the matrix |
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 |
public EigenvalueDecomposition(Matrix matrix)
matrix
- Square matrix
Structure to access D and V.Method Detail |
public Matrix getV()
public double[] getRealEigenvalues()
public double[] getImagEigenvalues()
public Matrix getD()
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