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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C#

C# 1.0 source.
hevd.csharp.zip - Eigenvalues and eigenvectors of a Hermitian matrix

C++

C++ source.
hevd.cpp.zip - Eigenvalues and eigenvectors of a Hermitian matrix
ablas.zip - optimized basic linear algebra subroutines with SSE2 support (for C++ sources only)

C++, multiple precision arithmetic

C++ source. MPFR/GMP is used.
GMP source is available from gmplib.org. MPFR source is available from www.mpfr.org.
hevd.mpfr.zip - Eigenvalues and eigenvectors of a Hermitian matrix
mpfr.zip - precompiled Win32 MPFR/GMP binaries

Delphi

Delphi source.
Can be compiled under FPC (in Delphi compatibility mode).
hevd.delphi.zip - Eigenvalues and eigenvectors of a Hermitian matrix

Visual Basic 6

Visual Basic 6 source.
hevd.vb6.zip - Eigenvalues and eigenvectors of a Hermitian matrix

Zonnon ^beta

Zonnon source.
Zonnon is an experimental language developed at ETH Zurich.
See www.zonnon.ethz.ch for more information.
hevd.zonnon.zip - Eigenvalues and eigenvectors of a Hermitian matrix