OK here is the problem

Suppose

im soo clueless =( any help would be awesome

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- February 4th 2011, 08:05 AMfizzle45Proving m=n in matrix problem
OK here is the problem

Suppose

im soo clueless =( any help would be awesome - February 4th 2011, 02:39 PMtopsquark
Here's a start. Let C be a p x m matrix. Then CA is a (p x m)(m x n) = p x n matrix. But CA = In. Thus C is an n x m matrix. Do this again for AD. What does all this mean for A?

-Dan

I fixed the problem. Unfortunately that makes my comment pointless.

-Dan - February 4th 2011, 03:16 PMAckbeet
Reply to topsquark:

Does that really work? I can see how you could get that C must be n x m, just to make the sizes work out. Why must it be n x n?

I think you're going to have to use rank arguments here. - February 4th 2011, 03:26 PMtopsquark
You are right. I had a small typo on the worksheet I scratched out the solution on. Apologies and thanks for the catch Ackbeet. 8]

-Dan - February 4th 2011, 04:46 PMAckbeet
The following facts may be useful:

and

Also, if is an matrix, it is true that

Furthermore, it is also true that

Using these facts, as well as facts about the minimum function, you should be able to prove both that and that thus proving your result.

Can you see your way forward?