A Matrix Fact
•
[Packard, 1994] Suppose
X, Y
Î
R
nxn
, and
X
=
X*
>0,
Y
=
Y
*>0.
Let
r
be a positive integer. Then there exist matrices
X
12
Î
R
nxr
, X
2
Î
R
rxr
such that
X
2
=X
2
*,
and
•
•
•
if and only if
w