Timeline for Is the matrix induced L1-norm greater than the induced L2-norm?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Oct 10, 2022 at 23:57 | comment | added | Oscar Lanzi | In fact the counterexample saturates the true bound I have added. | |
| Oct 10, 2022 at 22:21 | comment | added | Jochen Glueck | It might be worthwhile to add the following intuitive explanation of the phenomenon that is at work here: the problem is that a given norm on a vector space influences the induced norm (i.e., the operator norm, as my inner functional analyst wants to say) of an operator $A$ in two ways: in the expression $\|Ax\|$ over which we take a surpremum, and in the condition $\|x\| \le 1$ for taking the supremum. If you increase the norm on the vector space, the first point "wants" to increase the induced norm of $A$, while the second point "wants" to decrease it. | |
| Oct 10, 2022 at 22:03 | comment | added | Will Jagy | One point about induced norms on matrices, told me by Kahan decades ago: if we have two distinct induced norms, taking the maximum of those creates a new function on matrices with some nice properties, but it cannot be an induced norm itself. Oh: so no induced norm can dominate another. | |
| Oct 10, 2022 at 21:18 | vote | accept | DrunkCoder | ||
| Oct 10, 2022 at 21:11 | history | answered | Yemon Choi | CC BY-SA 4.0 |