Timeline for Eigenvalues of a partitioned self-adjoint matrix
Current License: CC BY-SA 3.0
10 events
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Oct 3, 2015 at 20:28 | comment | added | Majordomus | You are right, I just reacted to the previous comment. I have a complete knowledge of $A$ because it is $2\otimes2$ but $B_i$'s are arbitrary. Probably more accurately, my question was whether there can exist some 'decomposition' of $A'$ or just a 'simplification' in terms of the sublocks... Well, I guess that's it - if the rank of the $B_i$'s is greater than one, I really do not have much to say about $A'$. | |
| Oct 3, 2015 at 17:21 | comment | added | Carlo Beenakker | well sure, if you know the eigenvalues and eigenvectors of $B_i$ and $A$, then you have complete knowledge of $A'$ and so you can use any diagonalization algorithm to find its eigenvalues; but that's a trivial (and not particularly useful) statement, is that really your question? | |
| Oct 3, 2015 at 12:02 | comment | added | Majordomus | True, but with the knowledge of the eigenvalues of $B_i$ comes the knowledge of their eigenvectors (the same for $A$). So that's a lot of useful information that seems should lead at least to an estimate of the eigenvalues of $A'$. | |
| Oct 3, 2015 at 8:12 | comment | added | Carlo Beenakker | you might want to think of it like this: knowledge of the eigenvalues of $B_i$ doesn't tell you if $B_i$ has off-diagonal elements or not; but obviously that information is essential if you want to know the eigenvalues of $A'$; so obviously there cannot be "an algorithm for calculating the eigenvalues of $A'$ from the eigenvalues of $A$ and $B_i$". | |
| Oct 2, 2015 at 19:40 | comment | added | Carlo Beenakker | I'm afraid the answer is "no", knowledge of the eigenvalues of $B_i$ doesn't help if you seek the eigenvalues of $A'$. | |
| Oct 2, 2015 at 17:17 | history | edited | Majordomus | CC BY-SA 3.0 |
added 53 characters in body
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| Oct 2, 2015 at 17:10 | history | edited | Majordomus | CC BY-SA 3.0 |
correct link, fixed typo
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| Oct 2, 2015 at 15:54 | review | First posts | |||
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| Oct 2, 2015 at 15:51 | history | asked | Majordomus | CC BY-SA 3.0 |