Timeline for Solving $\text{trace}\left[\left(I + pY\right)^{-1} \left(I - p^{2}Y\right)\right] = 0$ for scalar $p$
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 22, 2017 at 18:51 | history | edited | Suvrit | CC BY-SA 3.0 |
removed a todo; added comment as part of the answer.
|
| Jan 19, 2017 at 2:50 | vote | accept | Abhishek Halder | ||
| Jan 18, 2017 at 22:51 | comment | added | Suvrit | using Rodrigo's observation and my comment to it, the above idea extends to general matrices by reducing them to upper triangular using Schur decomposition, and then solving an equation involving eigenvalues of the matrix $Y$ (which need not be diagonalizable any more). | |
| Jan 18, 2017 at 14:21 | comment | added | Igor Rivin | @AbhishekHalder Cool, I did NOT know this trick! | |
| Jan 18, 2017 at 5:50 | comment | added | Abhishek Halder | @IgorRivin: Since $X_{1}$ is symmetric positive definite, so is $X_{1}^{-1}$. Then we have this | |
| Jan 18, 2017 at 4:33 | comment | added | Igor Rivin | Why is the first statement true (that $Y$ is diagonalizable)? | |
| Jan 18, 2017 at 3:39 | history | answered | Suvrit | CC BY-SA 3.0 |