matrix theory question

G

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Let A =
[A11 (0) (0) ]
[A21 A22 (0) ]
[A31 A32 A33]
where A11 is r x r, A21 is s x r, A22 is s x s, A31 is t x r, A32 is t x s, A33 is t x t, and A11, A22, A33 are nonsingular; m = r + s + t.

Show that A^(-1) (A inverse) block lower triangular, find A^(-1) in terms of the matrices A11, A21, A22, A31, A32, and A33.

This problem is really hard and I have no idea how to solve it. Any help would greatly be appreciated.

Take care,
Beckie
Thank you!
 
Show that A<sup>-1</sup> block lower triangular.
Click to expand...
What does it mean for a matrix to "block" lower triangular? (I'm not familiar with this terminology, is why I ask.)

Would it be correct to assume that the "(0)" notation does not indicate three actual matrix entries, but instead means "all of the other entries above the diagonal are zeroes"? (Otherwise, r = s = t = 1 if A is square, is why I ask.)

Thank you.

Eliz.
 
Great question. Unfortunately, I have no idea. I'm so confused with this question. It is really tough.

Thanks for trying though. :)

Take care,
Beckie
 
I am pretty sure the 0's are not specific entries but are matrices of 0's of the appropriate sizes so that the entire matrix is square.
 
I got the answer for this problem. It wasn't as hard as I thought.

Beckie
 
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