Timeline for Lower-bound on smallest singular-value of rectangular random matrix
Current License: CC BY-SA 4.0
5 events
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| Sep 20, 2020 at 12:06 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Sep 20, 2020 at 8:31 | comment | added | dohmatob | Actually, Question 1 has an affirmative answer, $A=2$, for arbitrary $C>0$, and without any restriction on $\lambda$ other than $\lambda < 1$. See mathoverflow.net/a/372119/78539 | |
| Sep 18, 2020 at 13:48 | comment | added | dohmatob | OK, I see. I'm moving the discussion to a separate question mathoverflow.net/q/372015/78539. I really need the exponent to be $C$ (in order to absorb an entropy cost in the proof of something else I'm doing). Any input welcome! | |
| Sep 18, 2020 at 12:53 | comment | added | dohmatob | Thanks. Concerning the Tao et al. paper reference, I was referring to Q2. I read the paragraph just before 3.4 of this paper math.uci.edu/~rvershyn/papers/rv-ICM2010.pdf (Rudelson and Vershynin), and the authors say one can have $C=1$ in the subGaussian case, more precisely they claim: "if $n/N<1$, then there exists $c>0$ such that $ P(s_\min(A) \ge c\sqrt{N}) \ge 1 - 2e^{-N}$. Is this a typo ? | |
| Sep 17, 2020 at 20:49 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |