Timeline for Create matrix containing values in [0,1] where sum of all diagonals and anti-diagonals is fixed
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Apr 22, 2015 at 13:07 | history | edited | Tobias Springer | CC BY-SA 3.0 |
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| Apr 22, 2015 at 12:26 | answer | added | Noah Stein | timeline score: 1 | |
| Apr 22, 2015 at 11:15 | comment | added | user35593 | Choose all entries not on the main diagonal or main antidiagonal with random numbers. If the $a_i$ and $b_i$ satisfy the compatibility condition mentioned by Ilya Bogdanov you can complete this matrix such that it satisfies 2., 3. and 4. To get condition 1. you can use the idea of the comment of user35593. | |
| Apr 22, 2015 at 10:47 | comment | added | Ilya Bogdanov | These conditions are always dependent, and not only due to the sum of all elements. E.g., the sum of all elements with the even sum of indices can be expressed both via $a_i$ and via $b_i$. | |
| Apr 22, 2015 at 10:43 | comment | added | user35593 | If you have a solution you can choose two diagonals and two antidiagonals which intersect each other in four points, add a value to two of them and substract the same value to the other. The result is then again a solution. Maybe you can even build a new basis like this which makes the linear system easier. | |
| Apr 22, 2015 at 10:35 | comment | added | Tobias Springer | Yep, that's true, I know. And I suspect that it will crash at that point. I already thought about defining a multivariate function and applying BOBYQA in order to minimize it under the given constraints. However, I am still interested in similar problems with known solutions. | |
| Apr 22, 2015 at 9:57 | comment | added | Joonas Ilmavirta | If $n\in\{2,3\}$, you have more conditions than unknowns, so if the $a$s and $b$s don't satisfy some kind of a consistency condition, there is no solution. If $n=2$, then $a_{\pm1}$ and $b_{\pm1}$ determine the matrix uniquely and easily, but that matrix may not satisfy the other conditions. | |
| Apr 22, 2015 at 9:48 | review | First posts | |||
| Apr 22, 2015 at 9:57 | |||||
| Apr 22, 2015 at 9:47 | history | asked | Tobias Springer | CC BY-SA 3.0 |