Timeline for Probability for a random positive-semidefinite matrix to not be positive-definite?
Current License: CC BY-SA 3.0
4 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Nov 20, 2013 at 21:40 | vote | accept | Evgeni Sergeev | ||
| Nov 20, 2013 at 21:39 | comment | added | Evgeni Sergeev |
Right, in a small case we might have N=24 and n=3, so if we assume that the quantitative bound above is a good approximation to the actual probability cdf, which is probably a very bad assumption, then the probability of $|s_{min}| < 10^{-3}$ can be estimated to be around (where t0 = $\sqrt{N} - \sqrt{n}$) 2*exp(-(t0-1e-3)**2/2) - 2*exp(-(t0+1e-3)**2/2), which is 5.73e-24. Even if we're out by a factor of a trillion, that's still pretty good.
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| Nov 20, 2013 at 8:08 | history | answered | Dirk | CC BY-SA 3.0 |