Timeline for Spectrum of sum of weighted Wishart matrices
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Nov 27, 2020 at 21:42 | comment | added | jamblejoe | Thanks! I guess one can still make some use of that result by splitting the $c_j$'s into positive and negative and reduce the problem to the difference of just two wishart matrices. | |
| Nov 27, 2020 at 20:24 | comment | added | Carlo Beenakker | real or complex Wishart matrices is not an essential difference, the formulas will carry over; negative weights, however, is an essential difference; if you allow for negative weights the resulting matrix may no longer be positive definite, so this approximation of the weighted sum by an equivalent Wishart matrix will fail. | |
| Nov 27, 2020 at 16:51 | comment | added | jamblejoe | Another question: In the reference complex Wishart matrices are considered. I have not understood the proofs yet, so I can not say, in what sense they hold for real Wishart matrices as well. Or is this easily seen? | |
| Nov 27, 2020 at 16:49 | comment | added | jamblejoe | Thank you for the quick answer! I had a quick look into the reference you gave. There, the coefficients are assumed to be positive. I will see if I can generalize to real coefficients. | |
| Nov 27, 2020 at 12:21 | history | answered | Carlo Beenakker | CC BY-SA 4.0 |