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Symmetric Eigenproblems


The symmetric eigenvalue problem (SEP) is to find the eigenvalues  , tex2html_wrap_inline12778, and corresponding eigenvectors , tex2html_wrap_inline12780, such that
For the Hermitian eigenvalue problem  we have
For both problems the eigenvalues tex2html_wrap_inline12778 are real.

When all eigenvalues and eigenvectors have been computed, we write
where tex2html_wrap_inline12784 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.

Susan Blackford
Tue May 13 09:21:01 EDT 1997