Timeline for Derivative of complex matrix pseudo inverse with respect to real and imaginary components
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 8, 2018 at 15:32 | comment | added | Amit Kumar Jaiswal | As far as the function $\mathbf{Y^+}$ holomorphic and if in case the conjugate transpose $\mathbf{Y^*}$ of $\mathbf{Y}$ depends on Z, then their might be a possibility to calculate these derivatives. | |
| Aug 7, 2018 at 14:41 | comment | added | Joshua Meggitt | If $\mathbf{Y^+}$ is complex differentiable (which i am under the impression it is based on [Hjørungnes 2011] ), does this not mean by definition that the function is analytic? Or am i missing some subtlety... | |
| Aug 7, 2018 at 9:04 | comment | added | Carlo Beenakker | Cauchy-Riemann requires that the function you are differentiating depends on $z=x+iy$ but not on the conjugate $z^\ast$; since the pseudo inverse corresponds to the limit $Y^+=\lim_{\epsilon\rightarrow 0}(Y^\ast Y+\epsilon I)^{-1})Y^\ast$ involving the conjugate transpose $Y^\ast$ of $Y$, it would seem this requirement is violated. | |
| Aug 7, 2018 at 8:25 | review | Close votes | |||
| Aug 10, 2018 at 2:51 | |||||
| Aug 7, 2018 at 7:35 | review | First posts | |||
| Aug 7, 2018 at 8:07 | |||||
| Aug 7, 2018 at 7:34 | history | asked | Joshua Meggitt | CC BY-SA 4.0 |