The symmetric eigenvalue problem (SEP) is to find the eigenvalues ,
, and corresponding eigenvectors ,
, such that
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For the Hermitian eigenvalue problem we have
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For both problems the eigenvalues
are real.
When all eigenvalues and eigenvectors have been computed, we write
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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.