Timeline for A new method for processing music scores?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Aug 22, 2021 at 5:18 | comment | added | mathoverflowUser | also asked here since it might be more suited: stats.stackexchange.com/questions/541044/… | |
| Aug 21, 2021 at 19:41 | comment | added | mathoverflowUser | @CarloBeenakker: Sorry for not being to precise in the notation. This comes from first implementing it in python and then writing the equations later. | |
| Aug 21, 2021 at 19:40 | comment | added | Carlo Beenakker | confusing, in your post you say that $a,b$ are natural numbers, but it doesn't matter, the kernel $k_2(a,b)=\log a\log b$ is separable in the two arguments, so all eigenvalues are 0 except for a single eigenvalue equal to $\int_0^1 \log^2 x\, dx=2$. | |
| Aug 21, 2021 at 19:35 | comment | added | mathoverflowUser | @CarloBeenakker: $n,m$ should be positive real numbers $\le 1$. Is the matrix still positive semidefinite? | |
| Aug 21, 2021 at 19:33 | comment | added | Carlo Beenakker | let me see if I understand your first question: I construct the matrix $M$ with elements $M_{nm}=\log n \log m$ and $n,m=1,2,\ldots n_{\rm max}$; this matrix will have all eigenvalues equal to 0 except a single eigenvalue equal to $\lambda=\sum_{n=1}^{n_{\rm max}}\log^2 n$ --- so yes, it is positive semidefinite. | |
| Aug 21, 2021 at 18:50 | comment | added | mathoverflowUser | @CarloBeenakker: I updated the question with more details. I hope it is ok now, if not please do not hesitate to point to things which need clarification. | |
| Aug 21, 2021 at 18:49 | history | edited | mathoverflowUser | CC BY-SA 4.0 |
added 2951 characters in body
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| Aug 21, 2021 at 18:15 | comment | added | mathoverflowUser | @CarloBeenakker: I will update the question. | |
| Aug 21, 2021 at 17:37 | comment | added | Carlo Beenakker | you really need to formulate a math question (with equations) for this site. | |
| Aug 21, 2021 at 16:18 | review | Close votes | |||
| Sep 11, 2021 at 3:06 | |||||
| Aug 21, 2021 at 15:30 | history | asked | mathoverflowUser | CC BY-SA 4.0 |