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Results tagged with random-matrices
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user 166840
Statistics of spectral properties of matrix-valued random variables.
2
votes
0
answers
137
views
Expected value of number of collisions for a matrix valued random function
Consider the function
$$f(x_1, x_2, \ldots, x_k) = S_1^{x_1} S_2^{x_2} \cdots S_k^{x_k}.$$
Each $x_1, x_2, \ldots, x_k \in \{0, 1\}$ and each $S_i \in \mathbb{F}_q^{n \times n}$ is a randomly chosen …
2
votes
1
answer
383
views
Question about squaring a Haar random unitary
Consider an $n \times n$ unitary $U$, drawn from the Haar measure. I'm trying to find the distribution for $U^{2}$. Is it true that $U^{2}$ is also Haar random?
Note that for any fixed unitary $V$, $V …