Timeline for Minimal value of matrix norm induced by a norm
Current License: CC BY-SA 4.0
12 events
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| Mar 3, 2019 at 16:32 | history | edited | Jonas Adler | CC BY-SA 4.0 |
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| Mar 3, 2019 at 12:19 | vote | accept | Jonas Adler | ||
| Mar 3, 2019 at 11:31 | answer | added | Federico Poloni | timeline score: 5 | |
| Mar 3, 2019 at 11:18 | comment | added | Jochen Glueck | Thank you for the update. But what about nilpotent nonzero matrices? Those have spectral radius zero. | |
| Mar 3, 2019 at 11:17 | comment | added | Jonas Adler | I updated the proof of positive definiteness, the new one also gives an explicit bound. | |
| Mar 3, 2019 at 11:17 | history | edited | Jonas Adler | CC BY-SA 4.0 |
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| Mar 3, 2019 at 11:14 | comment | added | Jochen Glueck | By the way, sub-additivity is probably also going to be a problem since infima do not respect subadditivity, in general. | |
| Mar 3, 2019 at 11:11 | comment | added | Jochen Glueck | Well, I think the situation is actually a bit more involved. Multiplying the norm by a constant $a > 0$ is not really a problem since the constant $a$ cancels in the definition of the induced matrix norm. | |
| Mar 3, 2019 at 10:47 | comment | added | Jonas Adler | You are right, perhaps that is not at all true. I do think we could find such $c_1$, $c_2$ though, I'll have to look around for a proof. We would also have to "normalize" away a constant since the proof obviously fails by considering the family of norms $\|x\| = a \|x\|_2$ as $a \to \infty$. | |
| Mar 3, 2019 at 10:24 | comment | added | Jochen Glueck | I'm not sure I can follow your argument for positive definiteness. Why should $c_1$ and $c_2$ be independent of $X$? | |
| Mar 3, 2019 at 10:15 | history | edited | Jonas Adler | CC BY-SA 4.0 |
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| Mar 3, 2019 at 10:10 | history | asked | Jonas Adler | CC BY-SA 4.0 |