Timeline for Unitary condition
Current License: CC BY-SA 4.0
28 events
| when toggle format | what | by | license | comment | |
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| Nov 18, 2019 at 15:10 | history | edited | Toni Mhax | CC BY-SA 4.0 |
added 7 characters in body
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| Nov 18, 2019 at 13:57 | vote | accept | Toni Mhax | ||
| Nov 18, 2019 at 2:21 | history | edited | Toni Mhax | CC BY-SA 4.0 |
update statement
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| Nov 18, 2019 at 2:14 | history | edited | Toni Mhax | CC BY-SA 4.0 |
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| Nov 18, 2019 at 0:38 | comment | added | Toni Mhax | $\begin{pmatrix}\frac{\cos(\theta)}{\sqrt{2}}&-\frac{\sin(\theta)}{\sqrt{2}}&-\frac{\sqrt{2}}{2}\\\sin(\theta)& \cos(\theta)& 0\\\frac{(\cos\theta)}{\sqrt{2}}&-\frac{\sin(\theta)}{\sqrt{2}}&\frac{\sqrt{2}}{2}\end{pmatrix}$ but the bound isn't verified. | |
| Nov 17, 2019 at 21:23 | comment | added | Morgan Rogers | Consider $\begin{pmatrix}\frac{\cos(\theta)}{\sqrt{2}}&\frac{\sin(\theta)}{\sqrt{2}}&-\frac{\sqrt{2}}{2}\\ \sin(\theta)&\cos(\theta)&0\\ \frac{\cos(\theta)}{\sqrt{2}}&\frac{\sin(\theta)}{\sqrt{2}}&\frac{\sqrt{2}}{2}\end{pmatrix}$ for small $\theta > 0$... | |
| Nov 17, 2019 at 20:14 | comment | added | Toni Mhax | No you see 2) is independant of 1) i have no counterexample to 2) | |
| Nov 17, 2019 at 19:52 | comment | added | Morgan Rogers | Why are you exchanging the columns in the first part but permuting the basis in the second part? In my answer I assumed you meant up to a permutation of the columns in the same sense... | |
| Nov 17, 2019 at 18:38 | comment | added | Toni Mhax | Yes say $\begin{pmatrix}\frac{\sqrt{2}}{2}&0&-\frac{\sqrt{2}}{2}\\0&1&0\\\frac{\sqrt{2}}{2}&0&\frac{\sqrt{2}}{2}\end{pmatrix}$ up to a permutation similarity it is a direct sum of $1\oplus U_2$. And that's the second conjecture | |
| Nov 17, 2019 at 18:07 | comment | added | Morgan Rogers | Please could you give an example of where your "unless $U$ is a direct sum of $U_k$..." comment comes from? | |
| S Nov 17, 2019 at 16:25 | history | edited | Toni Mhax | CC BY-SA 4.0 |
Clarified some confusion observed in the comments
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| S Nov 17, 2019 at 16:25 | history | suggested | Morgan Rogers | CC BY-SA 4.0 |
Clarified some confusion observed in the comments
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| Nov 17, 2019 at 16:19 | answer | added | Morgan Rogers | timeline score: 2 | |
| Nov 17, 2019 at 15:56 | review | Suggested edits | |||
| S Nov 17, 2019 at 16:25 | |||||
| Nov 17, 2019 at 15:33 | history | edited | Toni Mhax | CC BY-SA 4.0 |
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| Nov 17, 2019 at 14:39 | history | edited | Toni Mhax | CC BY-SA 4.0 |
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| Nov 17, 2019 at 14:38 | comment | added | Sam Zbarsky | (2) is false even with the correction. Just perturb the identity matrix slightly. | |
| Nov 17, 2019 at 14:38 | comment | added | Toni Mhax | Yes thanks edited the question, thanks again | |
| Nov 17, 2019 at 14:37 | history | edited | Toni Mhax | CC BY-SA 4.0 |
Missed a text
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| Nov 17, 2019 at 12:28 | comment | added | YCor | There no problem for (1) with identity matrix. But I don't see how to interpret (2) "up to permutation". Please clarify. | |
| Nov 17, 2019 at 11:58 | history | edited | Toni Mhax | CC BY-SA 4.0 |
some tries on form and spacing
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| Nov 17, 2019 at 11:56 | comment | added | Toni Mhax | up to permutation | |
| Nov 17, 2019 at 11:56 | comment | added | kneidell | Actually, same goes for 2, unless I'm completely misunderstanding your question... | |
| Nov 17, 2019 at 11:55 | history | edited | Toni Mhax | CC BY-SA 4.0 |
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| Nov 17, 2019 at 11:54 | comment | added | kneidell | How does 1 fit with the identity matrix being unitary? | |
| Nov 17, 2019 at 11:51 | history | edited | Toni Mhax | CC BY-SA 4.0 |
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| Nov 17, 2019 at 11:44 | history | edited | Toni Mhax | CC BY-SA 4.0 |
typos
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| Nov 17, 2019 at 11:38 | history | asked | Toni Mhax | CC BY-SA 4.0 |