Timeline for Eigenvalues of the product of traceless unitary hermitian matrices
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 20, 2019 at 18:12 | comment | added | Gerson J Ferreira | Thanks! Indeed my conditions for A and B is not sufficient. I could rephrase the question to ask what are the conditions on A and B (beyond those already stated) that constrains S to have only non-real eigenvalues? But this seems difficult to answer. We'll try to work around this issue. Thanks again! | |
| Oct 19, 2019 at 8:51 | comment | added | Carlo Beenakker | @GersonJFerreira --- I have added a counterexample that meets the two criteria you added ($A$, $B$ noncommuting and not block diagonal). | |
| Oct 19, 2019 at 8:50 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
added 521 characters in body
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| Oct 18, 2019 at 21:48 | comment | added | Gerson J Ferreira | @FabianWirth, I agree. I've edited the question to improve the distinction between A and B. Let's consider then irreducible. In the block diagonal form is always possible to find a counter example. | |
| Oct 18, 2019 at 20:09 | comment | added | Fabian Wirth | This would not change the problem significantly. You can take Carlo's example as the first block of a block-diagonal example and add second diagonal blocks so that the overall matrices do not commute. The eigenvalues of the example here would still show up. | |
| Oct 18, 2019 at 19:47 | comment | added | Gerson J Ferreira | Thanks! In this case [A,B] = 0, I'll have to add this constraint... A and B cannot commute. | |
| Oct 18, 2019 at 18:41 | history | answered | Carlo Beenakker | CC BY-SA 4.0 |