Timeline for Are random circulant matrices almost orthonormal?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Nov 3, 2017 at 17:52 | comment | added | VSJ | Hi Bill, I'm not sure that is a mistake. Because even then, the eigenvalues will converge to 0 and not 1. Perhaps it is the case that the matrix is tending "pointwise" to identity, but it is not tending fast enough, and therefore the eigenvalues don't converge? | |
| Nov 3, 2017 at 13:33 | history | edited | Bill Bradley | CC BY-SA 3.0 |
Fixed mistake: rescaling down variance by $1/n$.
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| Nov 3, 2017 at 13:31 | comment | added | Bill Bradley | Ah, @VSJ , that is my mistake: I forgot to pass through the prefactor of $1/\sqrt(n)$ in the original definition of $M$. I will fix that now, at which point I think Marcel's answer is consistent with mine. | |
| Nov 2, 2017 at 4:04 | comment | added | VSJ | I'm confused about one part: Marcel's answer indicates that $MM^*$ is close to identity. Thus it should have eigenvalues close to 1? But your argument says eigenvalues are iid from a chi square distribution so they aren't all close to 1. How to reconcile these? | |
| Oct 16, 2017 at 12:42 | history | answered | Bill Bradley | CC BY-SA 3.0 |