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Results tagged with random-matrices
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user 46140
Statistics of spectral properties of matrix-valued random variables.
5
votes
Matrices over $\mathbb{F}_p$ that have nonzero determinant under any element permutation
$\det \begin{pmatrix} 1 \end{pmatrix} = 1$ works for any $p$.
$\det \begin{pmatrix} 0 & 1 \\ 1 & 1 \end{pmatrix} = -1$ similarly.
For $n=3$ we require $p \ge 5$. By exhaustion there's no solution for …
- 7,226
7
votes
Accepted
Is this combinatorial identity known? (of interest for random matrix theory)
Firstly, exploit the finite support to simplify the limits of the sums. Secondly, split the second sum. We get
$$\begin{align*}A(r,b) =& \sum\limits_{m=1}^{r} (2m-1) {r \choose b-m}{r \choose b+m-1} \ …
- 7,226