Timeline for How one can show that this matrix is full rank?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Jul 18 at 18:32 | history | edited | Stefano | CC BY-SA 4.0 |
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| Jul 18 at 18:02 | comment | added | Stefano | @ToniMhax done, I added them in the cased d=4,5,6, I hope now it is clearer, thank you! | |
| Jul 18 at 18:02 | history | edited | Stefano | CC BY-SA 4.0 |
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| Jul 18 at 16:37 | comment | added | Toni Mhax | Ok I guess I saw the pattern, but that was guessing i'll try to get that. (You can as I said just write those matrices for small values $d =4,5,6..$ this helps the reader). | |
| Jul 18 at 14:52 | comment | added | Stefano | @ToniMhax I edited the text and now the problem is written in all its generality. If you could give me some suggestion, I would be very thankful | |
| Jul 18 at 14:50 | history | edited | Stefano | CC BY-SA 4.0 |
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| Jul 15 at 6:48 | comment | added | Toni Mhax | This does not seem clear, for $A_i$ and $B_i$, say $j=2$ , is $A_i=\begin{pmatrix} -e_{i,2} & 0 & 1 & 0\\ 0&-e_{i,2} & 0 & 1 \end{pmatrix}$ ? If yes maybe $B_i$ expressions follows but the expression of $S_i$ is not very symmetrical, please recheck, giving examples in lower dimensions ($j=2$ or $3$) also helps. | |
| Jul 12 at 18:31 | answer | added | zeraoulia rafik | timeline score: -2 | |
| Jul 11 at 13:50 | history | edited | Stefano | CC BY-SA 4.0 |
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| Jul 11 at 11:31 | comment | added | Stefano | The generic problem is obtained considering not $e_{i,2},e_{i,3},e_{i,4}$ but $e_{i,j}$ for $j=2,\dots, d-1$ with the matrices changing as a consequence. And then you have to consider not just 8 blocks but $d+3$. Do you think that a computer algebra system could solve the problem for a generic d? | |
| Jul 11 at 11:10 | comment | added | Max Alekseyev | The tedious work for these particular matrices can be delegated to a computer algebra system. What is the generic problem? | |
| S Jul 11 at 10:21 | review | First questions | |||
| Jul 11 at 11:42 | |||||
| S Jul 11 at 10:21 | history | asked | Stefano | CC BY-SA 4.0 |