Timeline for Eigen problem with constrained (equal) eigenvalues
Current License: CC BY-SA 4.0
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| Feb 5, 2021 at 18:49 | comment | added | Louis Deaett | To your question, yes I think that is the thing left to determine, and it may depend on your application/context. The gist of Federico Poloni's answer is to choose this value so as to minimize the norm difference of your $\Omega$ and your $\tilde\Omega$, which is a natural idea. If you have more information from your application, then maybe something different makes sense. For example, maybe the application suggests that the two eigenvalues should not be given equal weight? I'm speculating, but there probably isn't more to say in full generality than what Federico has pointed out. | |
| Feb 5, 2021 at 9:11 | comment | added | meie73 | Thanks Louis for your reply. This was my first strategy to attack the problem. For sure, it is very simple and fast, but it is based on fixing the eigenvalues that are potentially equal to a value that I don't know. If from the statistical test I get the result that $k$ eigenvalues are equal, what shoud I do, fixing them to the average of these $k$ eigenvalues? Maybe, an iterative procedure could help in soving the problem, but I was wondering whether there was some analytical result in matrix algebra. Or maybe, some specific algorithm already treated in the literature. | |
| Feb 4, 2021 at 17:57 | history | answered | Louis Deaett | CC BY-SA 4.0 |