Module ojalgo
Package org.ojalgo.matrix.decomposition

Interface Eigenvalue.Spectral<N extends Comparable<N>>

All Superinterfaces:
DeterminantTask<N>, Eigenvalue<N>, InverterTask<N>, InvertibleFactor<N>, MatrixDecomposition<N>, MatrixDecomposition.Determinant<N>, MatrixDecomposition.EconomySize<N>, MatrixDecomposition.Hermitian<N>, MatrixDecomposition.Ordered<N>, MatrixDecomposition.RankRevealing<N>, MatrixDecomposition.Solver<N>, MatrixDecomposition.Values<N>, MatrixTask<N>, Provider2D, Provider2D.Condition, Provider2D.Determinant<N>, Provider2D.Eigenpairs, Provider2D.Inverse<Optional<MatrixStore<N>>>, Provider2D.Rank, Provider2D.Solution<Optional<MatrixStore<N>>>, SingularValue<N>, SolverTask<N>, Structure1D, Structure2D
All Known Implementing Classes:
HermitianEvD, HermitianEvD.C128, HermitianEvD.H256, HermitianEvD.Q128, HermitianEvD.R064, HermitianEvD.R128, RawEigenvalue.Symmetric
Enclosing interface:
Eigenvalue<N extends Comparable<N>>
public static interface Eigenvalue.Spectral<N extends Comparable<N>> extends Eigenvalue<N>, SingularValue<N>
“Spectral decomposition” refers specifically to the orthogonal/unitary eigen-decomposition of a normal matrix (most commonly Hermitian / symmetric).

Eigenvalue decomposition of a normal matrix = spectral decomposition.

If, in addition to the matrix being normal, all eigenvalues are real and nonnegative, then the matrix is positive semidefinite, and the decomposition coincides with the SVD. If some eigenvalues are negative, the decomposition is still valid, and can be tweaked to yield a valid SVD by taking absolute values of the eigenvalues and adjusting the signs of the corresponding eigenvectors (on one side).