The **symmetric eigenvalue problem (SEP)** is to find the **eigenvalues** ,
, and corresponding **eigenvectors** , , such that

For the **Hermitian eigenvalue problem** we have

For both problems the eigenvalues are real.

When all eigenvalues and eigenvectors have been computed, we write

where is a diagonal matrix whose diagonal elements are the
eigenvalues , and *Z* is an orthogonal (or unitary) matrix whose columns
are the eigenvectors. This is the classical **spectral factorization**
of *A*.

Two types of driver routines are provided for symmetric or Hermitian eigenproblems:

- a
**simple**driver (name ending -EV) , which computes all the eigenvalues and (optionally) the eigenvectors of a symmetric or Hermitian matrix*A*; - an
**expert**driver (name ending -EVX) , which can compute either all or a selected subset of the eigenvalues, and (optionally) the corresponding eigenvectors.

The driver routines are shown in table 3.4. Currently the only simple drivers provided are PSSYEV and PDSYEV.

Tue May 13 09:21:01 EDT 1997