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##

Deflating Subspaces

A *pair of right and left deflating subspaces* and
of have the same dimension and
satisfy and
for all , and furthermore
.
We also write this as
. The simplest
example is when is spanned by a single right eigenvector of
and is spanned by its image under and/or .
More generally a right deflating subspace may be spanned by a subset of
right eigenvectors of , and the left deflating
subspace by their images.
But since some pencils do
not have independent eigenvectors, there are right deflating subspaces
that are not spanned by eigenvectors.
For example, see the example in §2.5.2.

Susan Blackford
2000-11-20