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