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##

Singular Subspaces

A pair of -dimensional subspaces and are called
*(left and right) singular subspaces* of if
for all
and
for all . We also write this as
and
.

The simplest example is when and are spanned by
a single pair of singular vectors and of , respectively.
More generally, any pair of singular subspaces can be spanned by a subset of
the singular vectors of , although the spanning vectors do not have to
be singular vectors themselves.

Susan Blackford
2000-11-20