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##

Equivalences

Suppose and are nonsingular matrices.
Let
and
.
We say that the pencil
is
*equivalent* to and that
and are *equivalence transformations*.
and
have the same eigenvalues.
If () is a right (left) eigenvector of ,
then
(
)
is a right (left) eigenvector of
.

Susan Blackford
2000-11-20