Module ojalgo
Package org.ojalgo.matrix.decomposition

Class RawEigenvalue

java.lang.Object
org.ojalgo.matrix.decomposition.AbstractDecomposition<Double,R064Store>
org.ojalgo.matrix.decomposition.RawDecomposition
org.ojalgo.matrix.decomposition.RawEigenvalue
All Implemented Interfaces:
Eigenvalue<Double>, MatrixDecomposition<Double>, MatrixDecomposition.Determinant<Double>, MatrixDecomposition.Hermitian<Double>, MatrixDecomposition.Ordered<Double>, MatrixDecomposition.Values<Double>, Provider2D, Provider2D.Determinant<Double>, Provider2D.Eigenpairs, DeterminantTask<Double>, MatrixTask<Double>, Structure1D, Structure2D
Direct Known Subclasses:
RawEigenvalue.Dynamic, RawEigenvalue.General, RawEigenvalue.Symmetric
abstract class RawEigenvalue extends RawDecomposition implements Eigenvalue<Double>
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().