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## Proof that norm of submatrix must be less than norm of matrix it's embedded in

1. The problem statement, all variables and given/known data

http://dl.dropbox.com/u/4027565/2010-10-10_194728.png

2. Relevant equations

3. The attempt at a solution

||B|| = ||M_1 * A * M_2 ||

So from an equality following from the norm, we can get...

||B|| <= ||M_1||*||A||*||M_2||.

Now, we know that B is a submatrix of A. So if A is 4x3, then M_1 must be 1x4 and M_2 must be 3X1 (I know that block matrices are more complicated than that, but this might work). What this also means is that the combined product of M_1 and M_2 must be <= 1. But beyond that, I'm stuck. Is there another step I should take?

Thanks!
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