let $M_n(c)$ denote the n times n matrices over the complex number field. $N$ be a subspace of

$M_n(C)$.

1 If there is no unitary lies in $N$, what is the maximum of the dimension of $N$ can be?

It's easy to see that it is not less than n(n-1), I guess it's also tight, but I don't know if I am correct.

2 If all the rank of $M$ lies in $N$ are greater than a fixed integer $k$, what is the maximum of the dimension of $N$ can be?

`$\text{\LaTeX}$`

support. So there's really no excuse to have bad formatting. This looks cut-and-paste from something, what with the random line break in the first line. – Theo Johnson-Freyd Mar 30 '10 at 21:59visualpresentation of a question is what's important here. – Yemon Choi Mar 30 '10 at 22:30