Thread: Proving m=n in matrix problem

OK here is the problem
Suppose

im soo clueless =( any help would be awesome

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

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.

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

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?