q
A=A*
>0 and
B=B*
³
0. Then
A
>
B
iff
r
(
BA
-1
)<1.
q
Let
X=X*
³
0 be partitioned as
q
q
q
Then
Ker
X
22
Ì
Ker
X
12
. Consequently, if
X
22
+
is the pseudo-inverse
of
X
22
, then
Y
=
X
12
X
22
+
solves
q
YX
22
=
X
12
q
and
•