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##

Equivalences (Congruences)

Suppose is a nonsingular matrix.
Let
and
.
We say that the pencil
is
*congruent* to , and that
is a *congruence transformation*.
If and are Hermitian, with positive definite,
than and have these same properties.
Furthermore,
and
have the same eigenvalues, and if is an eigenvector
of , so that
, then
is an eigenvector of
.

Susan Blackford
2000-11-20