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Results tagged with random-matrices
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user 10265
Statistics of spectral properties of matrix-valued random variables.
8
votes
Expected norm of sum of random orthogonal matrices
EDIT: My answer only deals with the $d \to \infty$ regime.
This question is not too naive (or at least the answer is hard). I am almost sure that for fixed $d$ there is no exact formula. For the limi …
- 9,486
3
votes
Accepted
trace norm of AGB, where G is Gaussian random matrix
[Edit: Now I answer all questions.]
The answer to the first question is yes, the answer to the second question is no, and the answer to the third question is if and only if $p \geq 2$ (only a guess i …
- 9,486
13
votes
Accepted
Matrix inversion lemma with pseudoinverses
In fact more generally for any positive semidefinite matrix $A = \sum_{i=0}^k e_i e_i^T$ with $e_i$'s linearly independent, we have that $e_i^T B e_i = 1$, where $B$ is the Moore-Penrose pseudoinverse …
- 9,486
27
votes
Accepted
The probability for a symmetric matrix to be positive definite
Edit: According to Dean and Majumdar, the precise value of $c$ in my answer below is $c=\frac{\log 3}{4}$ (and $c=\frac{\log 3}{2}$ for GUE random matrices). I did not read their argument, but I have …
- 9,486