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Theorem 1
Proof:
Theorem 2 (inverse of a partitioned symmetric matrix)
Divide an symmetric matrix into four blocks
The inverse matrix can also be divided into four blocks:
Here we assume the dimensionalities of these blocks are:
 and are ,
 and are ,

and
are
with . Then we have
Proof:
i.e.,
Plug into to get
or
or
Applying theorem 1 to this expression, we also get the other expression in
the theorem. Similarly we can get
and
Theorem 3 (Determinant of a partitioned symmetric matrix)
Proof: Note that
The theorem is proved as we also know that
and
Next: Marginal and conditional distributions
Up: Appendix A: Conditional and
Previous: Appendix A: Conditional and
Ruye Wang
20061114