Timeline for Gradient of the trace of the logarithm of a product
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 13, 2018 at 11:05 | comment | added | Peter Michor | Write the series for $\log$ and differentiate each term: Differentiating a power needs $D_{A,X} A^n = XA^{n-1} + AXA^{n-2} +\dots+A^{n-1}X$ (for the directional derivative with respect to the variable $A$ in direction $X$), since the matrices do not commute. Passing to the gradient needs an inner product on the space of matrices. $\text{Tr}(XY^\top)$ is a suitable one. | |
| S Feb 13, 2018 at 10:35 | history | suggested | Rodrigo de Azevedo | CC BY-SA 3.0 |
Minor edits
|
| Feb 13, 2018 at 9:21 | review | Suggested edits | |||
| S Feb 13, 2018 at 10:35 | |||||
| Feb 13, 2018 at 3:22 | comment | added | Carlo Beenakker | unless $A=I$ this is a complicated calculation because you need to take the derivative of the logarithm of a matrix, see for example this MO question; for $A=I$ the answer is just ${\rm Tr}\,(1/G+1/G^t)$. | |
| Feb 13, 2018 at 0:06 | comment | added | Igor Rivin | What do you mean by "closed form"? | |
| Feb 12, 2018 at 23:40 | history | asked | Soheil Feizi | CC BY-SA 3.0 |