Timeline for Diagonalization of symmetric matrices of functions
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| May 17, 2023 at 9:04 | comment | added | Robert Bryant | @user1234567890: In the case that $\det G$ vanishes at an isolated point, this can be reduced to a topological question, because then the $(p,q)$-type of $G$ away from the isolated singularity must be constant, and you are essentially asking when a map from a punctured $m$-disk (which is homotopic to $S^{m-1}$) into the homogeneous space $\mathrm{GL}(n,\mathbb{R})/\mathrm{O}(p,q)$ can be lifted continuously to $\mathrm{GL}(n,\mathbb{R})$. | |
| May 17, 2023 at 5:29 | comment | added | user1234567890 | Thank you Robert. I'm surprised that this can not be done even continuously. Do you know if it has been studied under which conditions this can be done continuously? | |
| May 17, 2023 at 5:21 | vote | accept | user1234567890 | ||
| May 16, 2023 at 17:10 | history | edited | Robert Bryant | CC BY-SA 4.0 |
Added an argument to show that even the continuous case is impossible.
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| May 16, 2023 at 17:02 | history | edited | Robert Bryant | CC BY-SA 4.0 |
Added an argument to show that even the continuous case is impossible.
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| May 16, 2023 at 14:43 | history | edited | Robert Bryant | CC BY-SA 4.0 |
Expanded the argument to cover the true invertibility question.
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| May 16, 2023 at 12:31 | history | answered | Robert Bryant | CC BY-SA 4.0 |