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Results tagged with random-matrices
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user 297
Statistics of spectral properties of matrix-valued random variables.
7
votes
Accepted
Existence of a matrix with bounded entries and large smallest singular value
The OP wrote $[-1, 1]$ but refers to Hadamard matrices, whose entries are more strongly in $\{ -1, 1 \}$. Assuming that the former is meant, we can do this with the sine transform matrix. Take
$$M_{ab …
- 156k
34
votes
Accepted
Expected determinant of a random NxN matrix
As everyone above has pointed out, the expected value is $0$.
I expect that the original poster might have wanted to know about how big the determinant is. A good way to approach this is to compute $ …
- 156k
5
votes
Evaluation of a combinatorial sum (that comes from random matrices)
I may as well write down how I've been attacking this, although I don't have a solution yet. Sequences $(p_i)$ of nonnegative integers with sum $r$ are in bijection with weakly increasing $r$-tuples $ …
- 156k