Timeline for Explicit formula for this distance between positive semi-definite matrices?
Current License: CC BY-SA 4.0
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| Jun 13, 2020 at 12:21 | comment | added | dohmatob | Your problem can be reduced to that of computing the quantity $z(A,B) := \mathbb E_{\theta \sim \tau}[\|\theta\|_A\|\theta\|_B]$. This is because the other terms have trivial formulae, since they are expectations of quadratic forms of a random vector whose covariance matrix you know explicitly. I don't think you can compute $z(A,B)$ in closed-form for general $A$ and $B$. You can definitely obtain (possibly crude!) lower and upper bounds for $z(A,B)$ in terms of the eigenvalues of $A$ and $B$. | |
| S Feb 29, 2020 at 12:07 | history | suggested | Louis Deaett |
added tag linear-algebra
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| Feb 29, 2020 at 1:49 | review | Suggested edits | |||
| S Feb 29, 2020 at 12:07 | |||||
| Feb 27, 2020 at 18:31 | history | edited | YCor |
edited tags
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| Feb 27, 2020 at 17:47 | history | asked | Lénaïc Chizat | CC BY-SA 4.0 |