Eigenvalues and eigenvectors of a Hermitian matrix

Complex number λ and complex vector z are called an eigen pair of a complex matrix A, if Az = λz. If matrix A of size NxN is Hermitian, it has N eigenvalues (not necessarily distinctive) and N corresponding eigenvectors which form an orthonormal basis (generally, eigenvectors are not orthogonal, and their number could be less than N). For more information see description of the similar algorithm for real symmetric matrices.

Subroutine description

This algorithm finds all the eigenvalues (and, if needed, the eigenvectors) of a Hermitian matrix. The Hermitian matrix is reduced to real tridiagonal form by using orthogonal transformation. After that, the algorithm for solving this problem for a tridiagonal matrix is called. The algorithm is iterative, so, theoretically, it may not converge. In this case, it returns False.

This algorithm uses the subroutines from the LAPACK 3.0 library.

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