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

For the Hermitian eigenvalue problem  we have

For both problems the eigenvalues  are real.
 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.
 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.