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- Work out again the SVD theorem done in the class:
If is a real
matrix then here exist orthogonal
matrices
and
such that
where
and
.
- Suppose that
. Then show that
-
-
-
- If
,
and
, then
- Show that
-
-
- Let the SVD of be as above. If
and
then show that
- Show (without using condition numbers) that if is square (
) and
is
small, then solving A
is unstable.
- Show that in the norm
Subhashis Banerjee
2005-10-03