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##

Equivalences (Similarities)

Suppose is a nonsingular matrix.
Let .
We say that is
*similar* to
and that is a *similarity transformation*.
has the same eigenvalues as .
If is an eigenvector of , so that
, then
is an eigenvector of .

If is a unitary matrix, i.e., ,
we say is *unitarily similar* to .
If is real, we say orthogonal instead of unitary.

Susan Blackford
2000-11-20