Hi,

Define a matrix $\mathbf{A} \in \mathbb{R}^{m \times n}$ such that each element is independently and randomly chosen with probability 0.5 to be either +1, or -1. Do you know any result in the literature that talks about properties of this kind of matrices?

I have seen that there are some results for other kind of random matrices (for example matrices whose entries are i.i.d gaussian.) but not for this simple matrix of +1/-1.

I would be interested for example on the distribution of the $\sigma_{max}(A)$, (not in an asymptotic regime. $m$, $n$ are finite numbers and usually small in my case.)

Thank you very much for any pointer or any thoughts.

Best,

Alex

Howsmall are $m$ and $n$? Less than 10? Less than 100? – Yemon Choi May 1 '12 at 4:04