Timeline for Eigendecomposition after multiplying by diagonal matrix
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 15, 2011 at 12:59 | comment | added | Martin McCormick | Excellent, thanks that is very helpful! | |
| Jul 15, 2011 at 12:56 | vote | accept | Martin McCormick | ||
| Jul 14, 2011 at 17:25 | comment | added | David E Speyer | No and yes. It is not true that $e^{A} e^{B} = e^{A+B}$ so, if $A+B=C$, it need not be true that the eigenvalues of $e^A e^B$ are the exponentials of the eigenvalues of $e^C$. However, it is true that the set of all possible singular values of $e^A e^B$ is the exponential of the set of all possible eigenvalues for $A+B$. This is a theorem of Klyachko ams.org/mathscinet-getitem?mr=1799623 and it is discussed in section 11 of the refernce I give above. | |
| Jul 14, 2011 at 14:08 | comment | added | Martin McCormick | Thanks. Yes I came across Horn's stuff. So is this related because if you exponentiate the matrices it is addition of exponents as in the paper? | |
| Jul 14, 2011 at 12:53 | history | answered | David E Speyer | CC BY-SA 3.0 |