Timeline for $\sup \left\| A x + B y\right\|_2$ subject to $\left\|x\right\|_2 = \left\|y\right\|_2 = 1$
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Oct 16, 2018 at 0:53 | comment | added | Robin Zhang | Sorry, the last comment should have $\max_i \sum_{j=1}^k \lvert a_{i, j} \rvert$ for the row-sum norm. | |
| Oct 15, 2018 at 23:14 | history | edited | Robin Zhang | CC BY-SA 4.0 |
add note about generalization to general finite sums
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| S Oct 15, 2018 at 22:02 | history | suggested | MWB | CC BY-SA 4.0 |
dimensions seem flipped
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| Oct 15, 2018 at 21:59 | comment | added | Robin Zhang | The supremum norm isn't so esoteric! If both vector norms being considered are supremum norms, then the operator norm is just the row-sum maximum $\max_{i} \sum_{j = 1}^k a_{i,j}$. However, since we have both the Euclidean norm and the supremum norm, I'm not sure what the resulting operator norm should be. (You're right about the zeroes; I've just edited the expression in the answer to remove them. I must have had square matrices in my mind when writing that!) | |
| Oct 15, 2018 at 21:59 | review | Suggested edits | |||
| S Oct 15, 2018 at 22:02 | |||||
| Oct 15, 2018 at 21:51 | history | edited | Robin Zhang | CC BY-SA 4.0 |
remove redundant zeroes, clarify notation
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| Oct 15, 2018 at 4:32 | comment | added | MWB | The usual (Euclidean-induced) norm reduces to singular value decomposition. Are there similarly useful insights one can draw from the fact that this is an induced-norm problem (for a rather esoteric norm)? (BTW I don't think the 0s are needed in the block matrices) | |
| Oct 14, 2018 at 10:01 | history | answered | Robin Zhang | CC BY-SA 4.0 |