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.

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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