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## Generalized Symmetric Definite Eigenproblems (GSEP)

An expert driver is provided to compute all the eigenvalues and (optionally) the eigenvectors of the following types of problems:

where A and B are symmetric or Hermitian and B is positive definite. For all these problems the eigenvalues are real. When A and B are symmetric, the matrices Z of computed eigenvectors satisfy (problem types 1 and 3) or (problem type 2), where is a diagonal matrix with the eigenvalues on the diagonal. Z also satisfies (problem types 1 and 2) or (problem type 3). When A and B are Hermitian, the matrices Z of computed eigenvectors satisfy (problem types 1 and 3) or (problem type 2), where is a diagonal matrix with the eigenvalues on the diagonal. Z also satisfies (problem types 1 and 2) or (problem type 3).

The routine is listed in table 3.5.

Table 3.5: Driver routine for the generalized symmetric definite eigenvalue problems