**LA_GGEV** computes for a pair of real or complex matrices
the generalized eigenvalues in the form of scalar pairs (
)
and, optionally, the left and/or right generalized eigenvectors.

A generalized eigenvalue of the pair is, roughly speaking, a
scalar of the form
such that the matrix
is singular. It is usually represented as the pair
, as
there is a reasonable interpretation of the case
(even if ).

A right generalized eigenvector corresponding to a generalized
eigenvalue is a vector such
that
. A left generalized eigenvector is
a vector such that
, where is the
conjugate-transpose of .

The computation is based on the (generalized) real or complex Schur form of
. (See **LA_GGES** for details of this form.)

Susan Blackford 2001-08-19