# Eigensystems

This chapter describes functions for computing eigenvalues and eigenvectors of matrices. There are routines for real symmetric and complex hermitian matrices, and eigenvalues can be computed with or without eigenvectors. The algorithms used are symmetric bidiagonalization followed by QR reduction.

These routines are intended for "small" systems where simple algorithms are acceptable. Anyone interested finding eigenvalues and eigenvectors of large matrices will want to use the sophisticated routines found in LAPACK. The Fortran version of LAPACK is recommended as the standard package for linear algebra.

The functions described in this chapter are declared in the header file ``gsl_eigen.h'`.

- Real Symmetric Matrices
- Complex Hermitian Matrices
- Sorting Eigenvalues and Eigenvectors
- Eigenvalue and Eigenvector Examples
- Eigenvalue and Eigenvector References