Timeline for $2$-norm of idempotent matrix
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
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| Nov 29, 2021 at 15:53 | answer | added | Christian Remling | timeline score: 5 | |
| Nov 28, 2021 at 11:17 | answer | added | Fedor Petrov | timeline score: 3 | |
| Nov 28, 2021 at 10:42 | history | reopened |
abx Yemon Choi Andrés E. Caicedo Yoav Kallus Mateusz Kwaśnicki |
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| Nov 28, 2021 at 1:01 | comment | added | Yemon Choi | Also @AlexM. I agree with abx (my first interpretation of the question was yours, but then once I realized there are diagonal counterexamples I assumed that -- as is sometimes commonplace in matrix analysis -- $\Vert \cdot\Vert_p$ is used for the $\ell_p^n\to \ell_p^n$ norm. (The Hilbert-Schmidt norm is then often denoted, in those sources, by "F" for "Frobenius.) | |
| Nov 27, 2021 at 13:04 | comment | added | abx | @Alex M.: I think the OP meant the operator norm w.r.t. ${\lVert\ \rVert}_2$ on $\Bbb{C}^n$ — otherwise this is trivially false. | |
| Nov 27, 2021 at 12:35 | comment | added | Alex M. | @abx: I have no idea if one can come up with an even simpler proof than the one in the reference. On the other hand, please notice that here the OP asks about the norm $\| \cdot \| _2$ (i.e. $P$ is viewed as an $n^2$-dimensional vector), whereas in the reference one works with the operator norm. Maybe that proof can be adapted to this situation, I haven't tried. | |
| Nov 27, 2021 at 12:27 | comment | added | abx | @Alex M.: Is there a simpler proof in the finite-dimensional case? Anyway, I agree that this is not a research question. But I have seen more elementary questions well-received on MO... | |
| Nov 27, 2021 at 11:14 | comment | added | Alex M. | @abx: I beg to disagree: the proof in that reference is ingenious, but entirely elementary. Furthermore, things are easier in this post because the Hilbert space is finite-dimensional, so in principle one has more ways of attacking the problem. This is definitely a good question for MSE, undoubtedly, but maybe less so for MO. | |
| Nov 27, 2021 at 9:27 | review | Reopen votes | |||
| Nov 28, 2021 at 10:47 | |||||
| Nov 27, 2021 at 9:26 | comment | added | abx | I don't understand why this question is closed. This is nontrivial, see the nice reference given by Christian Remling. | |
| Nov 27, 2021 at 9:18 | history | closed |
Benjamin Steinberg Jon Bannon Mikael de la Salle Stefan Kohl♦ |
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| Nov 27, 2021 at 8:56 | history | edited | Rodrigo de Azevedo | CC BY-SA 4.0 |
added 20 characters in body
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| Nov 26, 2021 at 13:35 | review | Close votes | |||
| Nov 27, 2021 at 9:19 | |||||
| Nov 26, 2021 at 13:32 | comment | added | Louis Deaett | What makes you think the equation does hold? | |
| Nov 26, 2021 at 13:31 | comment | added | Christian Remling | See here: math.nthu.edu.tw/~amen/2014/131012(final).pdf | |
| Nov 26, 2021 at 13:09 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| S Nov 26, 2021 at 12:42 | review | First questions | |||
| Nov 26, 2021 at 13:26 | |||||
| S Nov 26, 2021 at 12:42 | history | asked | ForeverHaibara | CC BY-SA 4.0 |