Timeline for Is it possible to decompose a symmetric, positive definite matrix in this way?
Current License: CC BY-SA 2.5
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 17, 2011 at 1:53 | vote | accept | JMS | ||
| Jan 17, 2011 at 1:53 | comment | added | JMS | Yes, that works. An example, for posterity: $\Sigma =\left( \begin{array}{cc} s & v' \\ v & T \end{array} \right) = \left( \begin{array}{cc} \sqrt{s} & 0 \\ v/\sqrt{s} & I_{p-1} \end{array} \right) \left( \begin{array}{cc} 1 & 0 \\ 0 & T - vv'/s \end{array} \right) \left( \begin{array}{cc} \sqrt{s} & v'/\sqrt{s} \\ 0 & I_{p-1} \end{array} \right)$ It just remains to show that $T - vv'/s$ is positive definite, which is not difficult (and I guess also that it isn't diagonal in order to fit my original problem statement). | |
| Jan 17, 2011 at 0:38 | history | answered | Igor Rivin | CC BY-SA 2.5 |