Class HermitianEvD<N extends Comparable<N>>

java.lang.Object
org.ojalgo.matrix.decomposition.AbstractDecomposition<N, DecompositionStore<N>>
org.ojalgo.matrix.decomposition.DenseEigenvalue<N>
org.ojalgo.matrix.decomposition.HermitianEvD<N>
All Implemented Interfaces:
Eigenvalue<N>, Eigenvalue.Spectral<N>, MatrixDecomposition<N>, MatrixDecomposition.Determinant<N>, MatrixDecomposition.EconomySize<N>, MatrixDecomposition.Hermitian<N>, MatrixDecomposition.Ordered<N>, MatrixDecomposition.RankRevealing<N>, MatrixDecomposition.Solver<N>, MatrixDecomposition.Values<N>, SingularValue<N>, Provider2D, Provider2D.Condition, Provider2D.Determinant<N>, Provider2D.Eigenpairs, Provider2D.Inverse<Optional<MatrixStore<N>>>, Provider2D.Rank, Provider2D.Solution<Optional<MatrixStore<N>>>, DeterminantTask<N>, InverterTask<N>, MatrixTask<N>, SolverTask<N>, InvertibleFactor<N>, Structure1D, Structure2D
Direct Known Subclasses:
HermitianEvD.C128, HermitianEvD.H256, HermitianEvD.Q128, HermitianEvD.R064, HermitianEvD.R128
abstract class HermitianEvD<N extends Comparable<N>> extends DenseEigenvalue<N> implements Eigenvalue.Spectral<N>
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().