Timeline for Symmetric tensor components
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| May 22, 2020 at 11:08 | vote | accept | Zarathustra | ||
| S May 22, 2020 at 11:08 | history | suggested | Alex Ravsky |
Added a tag.
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| May 22, 2020 at 10:33 | review | Suggested edits | |||
| S May 22, 2020 at 11:08 | |||||
| May 22, 2020 at 10:32 | answer | added | Alex Ravsky | timeline score: 0 | |
| May 20, 2020 at 12:33 | history | edited | Zarathustra | CC BY-SA 4.0 |
deleted 107 characters in body
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| May 18, 2020 at 16:02 | comment | added | Zarathustra | Yes, but what is confusing me is the notation $dist(i,j,k,l)$, is this supposed to represent pair-wise distances between the integers? For the case of a matrix, this would mean that elements of distance $|i-j|>N$ away from the diagonal are zero. | |
| May 18, 2020 at 15:50 | comment | added | Zach Teitler | So, you want to count the set of integer $4$-tuples $(i,j,k,l)$ with $|i|,|j|,|k|,|l|,|i-j|,\dotsc,|k-l|\leq N$, modulo the equivalence relation $(i,j,k,l)\sim(i+b,j+b,k+b,l+b)$? | |
| May 18, 2020 at 13:05 | review | Close votes | |||
| Jun 3, 2020 at 3:03 | |||||
| May 18, 2020 at 13:04 | history | edited | Zarathustra | CC BY-SA 4.0 |
added 461 characters in body
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| May 18, 2020 at 13:00 | comment | added | Zarathustra | I forgot to add that the tensor must satisfy $dist(i,j,k,l)\leq N$. This is also confusing me, as what is meant here by dist(i,j,k,l) is meant by the pair combinations of indices, so $|i-j|\leq N$ , $|i-k|\leq N$. $|i-l|\leq N$ ... and so on. Also, the matrix is required to satisfy the symmetry above with $|i-j| \leq N$. In that case, you can fix one of the matrix indices $i$ and compute a single row; the rest follows by symmery but this is what I don't see in the tensor case | |
| May 18, 2020 at 12:48 | comment | added | Ben McKay | It is not true; you are only allowing simultaneous addition to all indices at once, not each index separately. Think again about matrices (which, in your setting, are I suppose of infinite dimension). Draw matrix entry $C_{ij}$ at position $(i,j)$. Your symmetry allows you to equate entries as you move by a vector $(r,r)$ in the plane, not by $(0,r)$ or $(r,0)$. | |
| May 18, 2020 at 12:41 | history | asked | Zarathustra | CC BY-SA 4.0 |