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Results tagged with random-matrices
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user 8430
Statistics of spectral properties of matrix-valued random variables.
8
votes
1
answer
1k
views
Expected norm of sum of random orthogonal matrices
Somehow I got wondering about the following question today:
Suppose $Q_1,\ldots,Q_n$ are random (uniformly sampled) $d \times d$ orthogonal matrices.
What is the expected value of the quantity $\ …
- 28.6k
12
votes
1
answer
3k
views
Matrix inversion lemma with pseudoinverses
The utility of the Matrix Inversion Lemma has been well-exploited for several questions on MO. Thus, with some positive hope, I'd like to field a question of my own.
Suppose we pick $n$ values $x_1,\ …
- 28.6k
19
votes
1
answer
2k
views
Smallest eigenvalue of a tricky random matrix
While experimenting with positive-definite functions, I was led to the following:
Let $n$ be a positive integer, and let $x_1,\ldots,x_n$ be sampled from a zero-mean, unit variance gaussian. Consider …
- 28.6k