Timeline for Can we perturb a map $\mathbb{R}^n \to \mathbb{R}^n$ to have distinct singular values?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Nov 20, 2019 at 11:34 | history | edited | Asaf Shachar | CC BY-SA 4.0 |
I have cl
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| Nov 20, 2019 at 11:02 | vote | accept | Asaf Shachar | ||
| Nov 17, 2019 at 14:38 | history | edited | Asaf Shachar | CC BY-SA 4.0 |
added 94 characters in body
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| Nov 13, 2019 at 10:00 | history | edited | Asaf Shachar | CC BY-SA 4.0 |
I have added a possible strategy
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| S Nov 11, 2019 at 12:47 | history | bounty ended | Asaf Shachar | ||
| S Nov 11, 2019 at 12:47 | history | notice removed | Asaf Shachar | ||
| Nov 9, 2019 at 19:31 | answer | added | Dap | timeline score: 3 | |
| S Nov 9, 2019 at 16:56 | history | bounty started | Asaf Shachar | ||
| S Nov 9, 2019 at 16:56 | history | notice added | Asaf Shachar | Draw attention | |
| Nov 9, 2019 at 16:37 | comment | added | Lev Soukhanov | I'm not really sure but I feel the answer should be ''no'', because consider the following map from 3-dimensional ball: $f: (x; y; z) \rightarrow (- 1000 x(1 + x^2 + y^2); - 1000 y (1 + x^2 + y^2); -z)$ consider the map $df^t df$ (from the ball to the space of symmetric matrices). Matrices with $\sigma_1 = \sigma_2 < 0$ form a family of codimension two, and I believe that this thing intersects it transversely. Hence, it won't be possible to smoothly perturb it to remove the intersection. | |
| Nov 9, 2019 at 11:05 | history | edited | Asaf Shachar | CC BY-SA 4.0 |
I have added a section regarding my motivation.
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| Nov 9, 2019 at 8:32 | history | edited | Asaf Shachar | CC BY-SA 4.0 |
I have made my assumptions stronger
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| Oct 11, 2019 at 9:17 | history | asked | Asaf Shachar | CC BY-SA 4.0 |