Timeline for Eigenvalues of the sum of a diagonal and a unit matrix
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 29, 2018 at 17:28 | comment | added | Federico Poloni | To avoid confusing future readers: note that this answer does not provide a way to compute the eigenvalues, as asked, but only an expression for the characteristic polynomial. | |
| Apr 29, 2018 at 14:37 | comment | added | Christo | Could you explain this further, with J being arbitrary rank one matrix. And how to compute the eigen values in that case? | |
| Jul 19, 2012 at 22:54 | comment | added | Chris Godsil | @Jess: I have no intuition for $\phi(D,t)-\phi'(D,t)$. The ratio $\phi'(M,t)/\phi(M,t)$ turns up in combinatorics in various places. I am not sure I really understand what "usefulness" means here. | |
| Jul 18, 2012 at 14:38 | comment | added | Jess Riedel | @Denis: Could you say another word or two about making the connection to the Sherman--Morrison formula? I see that $J$ here is a particular rank-one matrix, but I don't see what this has to do with calculating an inverse $(D+J)^{-1}$ where $D^{-1}$ is already known. I can generalize the above answer for arbitrary rank-one $J$, but then the sum has no obvious interpretation. @Chris, is there intuition for the RHS, $\phi(D,t)-\phi'(D,t)$? What's the usefulness of a derivative of a characteristic function? | |
| Jun 16, 2011 at 14:22 | comment | added | Denis Serre | Well, $J$ is a rank-one matrix. So this calculation is nothin but a special case of the Sherman--Morrison formula. | |
| Jun 16, 2011 at 13:11 | comment | added | Peter Cudmore | Thanks very much, this was exactly what i was looking for. | |
| Jun 16, 2011 at 13:09 | vote | accept | Peter Cudmore | ||
| Jun 16, 2011 at 12:39 | history | edited | Chris Godsil | CC BY-SA 3.0 |
added 3 characters in body
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| Jun 16, 2011 at 12:17 | history | answered | Chris Godsil | CC BY-SA 3.0 |