Timeline for Are $n \times n$ special orthogonal matrices, all the entries of which have the same absolute value, possible for $n \neq 4$?
Current License: CC BY-SA 4.0
11 events
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| Feb 3, 2020 at 15:59 | history | edited | Francois Ziegler | CC BY-SA 4.0 |
added 356 characters in body
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| Feb 3, 2020 at 5:19 | history | edited | Francois Ziegler | CC BY-SA 4.0 |
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| Feb 3, 2020 at 4:57 | history | edited | Francois Ziegler | CC BY-SA 4.0 |
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| Feb 3, 2020 at 4:52 | history | edited | Francois Ziegler | CC BY-SA 4.0 |
added 410 characters in body
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| Feb 3, 2020 at 0:46 | comment | added | Paul B. Slater | OK, point well-taken, FZ. So, my conjecture should be for integers that are not powers of 2, rather than integers that are not multiples of 4. | |
| Feb 3, 2020 at 0:38 | comment | added | Francois Ziegler | @PaulB.Slater I double the size each time, so I think it solves only powers of 2 — your own arises that way starting from the 1$\times$1 identity. But yes, if you now want to exclude those it actually shouldn’t be by changing the question but by asking another. (Else no one knows who’s been answering what.) | |
| Feb 3, 2020 at 0:29 | comment | added | Paul B. Slater | Hasn't the $n \in 4 \mathbf{Z}$ case been settled by the answer of Ziegler, given that the orginal $4 \times 4$ $Q$ is in SO(n)? | |
| Feb 3, 2020 at 0:25 | comment | added | Paul B. Slater | OK--thanks for the answer! So, how about a conjecture on my part that for $m$ not a multiple of 4, one can not have an SO(m) matrix, with the entries of the $m$-th row and column all equal and positive, and all the remaining entries of the same absolute value as the entries of the last row and column. So, Hadamard matrices would be special in this regard. | |
| Feb 3, 2020 at 0:21 | history | edited | Francois Ziegler | CC BY-SA 4.0 |
Fulfill condition on last row & column
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| Feb 3, 2020 at 0:11 | comment | added | LSpice | Unfortunately it's only in the comments, but @PaulB.Slater has revised the question to require that $n$ not be a multiple of $4$. | |
| Feb 2, 2020 at 23:58 | history | answered | Francois Ziegler | CC BY-SA 4.0 |