Timeline for Matrix derivative with respect to the pseudo-inverse
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| S May 19, 2015 at 8:02 | history | suggested | alexsuse | CC BY-SA 3.0 |
The first line contained a typo which obscured the answer. The answer doesn't make sense if f is the inverse matrix function.
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| May 19, 2015 at 7:21 | review | Suggested edits | |||
| S May 19, 2015 at 8:02 | |||||
| Feb 3, 2015 at 17:49 | comment | added | alexsuse | Such snark, much calculus :D. FWIW, I think you meant $u(A) = A^{-1}$ in the first line. At least it makes more sense that way. And technically speaking, you didn't show that my formula is false. My formula is written in terms of $A^{-1}$, so it is only natural that it would not hold if $A$ is not invertible (that is actually part of my question). That being said, thanks for the comments. | |
| Sep 13, 2014 at 12:57 | history | edited | loup blanc | CC BY-SA 3.0 |
added 818 characters in body
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| Sep 12, 2014 at 11:36 | comment | added | loup blanc | @ alexsuse, $Du_{A^{-1}}$ is the derivative of $u:X\rightarrow X^{-1}$ in $A^{-1}$; it is a linear application that is defined on $M_n(\mathbb{R})$ with values in $M_n(\mathbb{R})$. The derivative of the function composition is $Dg_{A^{-1}}=Df_A\circ Du_{A^{-1}}$. My last formula is obtained when we compose with any function $t\rightarrow A^{-1}(t)$. Instead of reading the Matrix Cookbook, read a good book about differential calculus. | |
| Sep 12, 2014 at 10:57 | comment | added | alexsuse | Not sure what you meant. What is $u$ in your notation, and what do you mean by the $Du_{A^{-1}}:H$ notation? Note that I'm considering the derivative of a matrix with respect to another matrix. In that sense, $df/dA$ is a matrix ($(df/dA)_{ij} = \frac{\partial f}{\partial A_{ij}}$), and so is $df/d(A^{-1})$. In your example, I think you are considering a matrix which is a function of a parameter and looking at the derivative with respect to that parameter. | |
| Sep 11, 2014 at 9:16 | review | Low quality posts | |||
| Sep 11, 2014 at 10:03 | |||||
| Sep 10, 2014 at 23:56 | history | answered | loup blanc | CC BY-SA 3.0 |