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##

Equivalences

Suppose and are *unitary matrices*, i.e.,
and .
If and are real, then and ,
and we call them
*orthogonal matrices*. Let .
We say that is
*unitarily (orthogonally) equivalent* to
and that and are *unitary (orthogonal)
equivalence transformations*.
has the same singular values as .
If and are left and right singular vectors of , respectively,
so that and
, then and are
left and right singular vectors of , respectively.

Susan Blackford
2000-11-20