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### Symmetric Eigenproblems

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.