Timeline for How to find bounds on the eigenvalues of a matrix?
Current License: CC BY-SA 4.0
11 events
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| Feb 9, 2021 at 10:55 | comment | added | Charlotte | @user64494; I understand that but the question has to be done without numeric, it needs to be proved. | |
| Feb 9, 2021 at 8:17 | comment | added | user64494 | @Math_Freak: Numeric mathis apart of math, like or dislike it, | |
| Feb 9, 2021 at 2:29 | comment | added | Charlotte | @CarloBeenakker; is there any trick by which it can be proved mathematically without using any numerical computation | |
| Feb 9, 2021 at 2:28 | comment | added | Charlotte | @user64494; thanks for your efforts, but the problem needs to be proved mathematically and not through any software like Mathematica | |
| Feb 8, 2021 at 21:37 | history | edited | user64494 | CC BY-SA 4.0 |
added 108 characters in body
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| Feb 8, 2021 at 21:35 | comment | added | user64494 | @CarloBeenakker: Thank you. Fixed. | |
| Feb 8, 2021 at 21:31 | comment | added | Carlo Beenakker | the matrix of the OP has $2(n-2)$ and not $2n-2$ as in your Mathematica code | |
| Feb 8, 2021 at 21:27 | comment | added | user64494 |
@CarloBeenakker: Yes, f[62605783003825957106601552641839576616084246664423713800192, 4] produces $-2.67282$ and m = 62605783003825957106601552641839576616084246664423713800192; n = 4;Eigenvalues[{{0, m - 1, 2, n - 1}, {1, m - 2, 1, n - 1}, {2, m - 1, 0, 2 n - 2}, {1, m - 1, 2, 2 n - 2}}] // N results in $\{155.857,21.113,-2.58165,-0.388454\}$.
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| Feb 8, 2021 at 21:08 | comment | added | Carlo Beenakker | but $-2.67282$ is greater than $-3$, so you are saying the claim of the OP is false? the value for $m$ where this sum is reached seems so astronomically large, it looks suspiciously like an issue of too little numerical accuracy | |
| Feb 8, 2021 at 20:53 | comment | added | user64494 |
For example, n = 61; m = 56; Eigenvalues[{{0, m - 1, 2, n - 1}, {1, m - 2, 1, n - 1}, {2, m - 1, 0, 2 n - 2}, {1, m - 1, 2, 2 n - 2}}] // N performs $\{155.857,21.113,-2.58165,-0.388454\}$.
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| Feb 8, 2021 at 20:49 | history | answered | user64494 | CC BY-SA 4.0 |