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Results tagged with operator-norms
Search options questions only
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user 9924
5
votes
0
answers
390
views
An operator-norm version of Siegel's Lemma
Is there a kind of Siegel's Lemma saying that if $M$ is a ``small-height'' integer matrix, then there is a "small-height" vector $x$ with $\|Mx\|=\|M\|\|x\|$? (Here $\|Mx\|$ and $\|x\|$ denote the Euc …
- 23k
19
votes
1
answer
901
views
Is the norm of a $0-1$ matrix (almost) attained on a $0-1$ vector?
I'd like to state explicitly a problem which was somehow hidden in my three-week-old post:
Does there exist an absolute constant $c>0$ with the property that for any matrix $M\in{\mathcal M}_{m\ti …
- 23k
2
votes
1
answer
930
views
Approximation with a rank-$1$ matrix
Given a matrix $A$ (generally speaking, complex and non-square), I want to find an identically-sized matrix $D$ with ${\rm rk} D\le 1$ to minimize the induced operator norm $\|A-D\|_2$. From the Singu …
- 23k
6
votes
2
answers
398
views
$\|T\|_2 \le \sqrt{\|T\|_1\|T\|_\infty}$
Let $T$ be a linear operator acting on a finite-dimensional real or complex
vector space. As a direct consequence (or rather a particular case) of the
Riesz-Thorin theorem, we have
$$ \|T\|_2 \le \s …
- 23k