Timeline for Lower bound $x^TSA^TASx$
Current License: CC BY-SA 3.0
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| Jul 7, 2017 at 19:58 | comment | added | Robert Israel | $x \cdot 1 = 0$ seems not particularly helpful, nor the maximum entry of $x$: maybe $x$ has two entries of $+M$ and $-M$ and all the rest $0$. Then $\sum_j S_jj x_j^2$ is $M^2$ times a Binomial($2,1/2$) random variable, which has probability $1/4$ of being $0$. If you want a nontrivial lower bound with high probability, you'll need to rule out the possibility that nearly all entries of $x$ are very close to $0$. | |
| Jul 7, 2017 at 18:47 | comment | added | johnny | @Thank you for the reply. I know some information about $x$, $x\cdot 1=0$ and I have a bound for the maximum entry of $x$. I was hoping to use a concentration inequality to be able to lower bound it. | |
| Jul 7, 2017 at 17:52 | history | answered | Robert Israel | CC BY-SA 3.0 |