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Results tagged with random-matrices
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user 2807
Statistics of spectral properties of matrix-valued random variables.
11
votes
Expected determinant of a random NxN matrix
For some further results of this nature, see Exercise 5.64 of Enumerative Combinatorics, vol. 2. This exercise deals with the uniform distribution on (0,1)-matrices or $(-1,1)$-matrices, but the argum …
- 50.8k
6
votes
Accepted
Expected value of determinant of simple infinite random matrix
Here is a solution to Hipstpaka's question about $\det(A)^2$. I don't
have enough space to answer in a comment. I don't know where a
statement appears in the literature, but the proof uses a standard
…
- 50.8k
16
votes
Accepted
Expected size of determinant of $AA^T$ for non-square random $A$
By the Cauchy-Binet theorem, $\det AA^T=\sum (\det B)^2$, where $B$
ranges over all $m\times m$ submatrices of $A$. The expected value of
$(\det B)^2$ is $(m+1)!/4^m$, so the expected value of $\det A …
- 50.8k