Timeline for Eigenvalues two-fold degenerate
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 3, 2023 at 14:04 | comment | added | Carlo Beenakker | see also mathoverflow.net/q/446048/11260 | |
| May 3, 2023 at 9:10 | vote | accept | António Borges Santos | ||
| May 3, 2023 at 1:03 | answer | added | can't stop me now | timeline score: 1 | |
| May 3, 2023 at 0:51 | comment | added | Christian Remling | Induction on the size of the matrix should work too. | |
| May 3, 2023 at 0:49 | comment | added | Christian Remling | The coefficient of $\lambda^k$ is the sum of determinants of smaller matrices, and these are singular when $k$ is odd. (For example, in the $4\times 4$ case, the coefficient of $\lambda$ comes from the $3\times 3$ submatrices obtained by deleting the $k$th row and column.) | |
| May 3, 2023 at 0:43 | comment | added | António Borges Santos | how do you see that it is even? | |
| May 3, 2023 at 0:42 | comment | added | Christian Remling | I think it's quite easy to see that (in the even-dimensional case) the characteristic polynomial is even, so the eigenvalues of $A$ come in pairs $\pm \lambda$. (In odd dimensions, it is odd, and the conclusions are the same.) | |
| May 2, 2023 at 23:08 | history | asked | António Borges Santos | CC BY-SA 4.0 |