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Public Member Functions | |
| EigenvalueDecomposition (Matrix Arg) | |
| Matrix | getV () |
| double[] | getRealEigenvalues () |
| double[] | getImagEigenvalues () |
| Matrix | getD () |
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().
| Jama.EigenvalueDecomposition.EigenvalueDecomposition | ( | Matrix | Arg | ) |
Check for symmetry, then construct the eigenvalue decomposition
| A | Square matrix |
| Matrix Jama.EigenvalueDecomposition.getD | ( | ) |
Return the block diagonal eigenvalue matrix
| double [] Jama.EigenvalueDecomposition.getImagEigenvalues | ( | ) |
Return the imaginary parts of the eigenvalues
| double [] Jama.EigenvalueDecomposition.getRealEigenvalues | ( | ) |
Return the real parts of the eigenvalues
| Matrix Jama.EigenvalueDecomposition.getV | ( | ) |
Return the eigenvector matrix
1.8.7
