Timeline for Reconstruct a matrix from its traces
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Apr 30, 2019 at 15:13 | vote | accept | yarchik | ||
| Apr 30, 2019 at 12:34 | history | became hot network question | |||
| Apr 30, 2019 at 12:17 | answer | added | fedja | timeline score: 12 | |
| Apr 30, 2019 at 11:20 | history | edited | yarchik | CC BY-SA 4.0 |
The formulation was vague on several points. Now they are all made more precise thanks to users' comments.
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| Apr 30, 2019 at 10:01 | history | edited | yarchik | CC BY-SA 4.0 |
fixed wording
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| Apr 30, 2019 at 9:59 | history | edited | Martin Sleziak |
added the (traces) tag
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| Apr 30, 2019 at 9:58 | history | edited | yarchik | CC BY-SA 4.0 |
The question is made more precise.
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| Apr 30, 2019 at 9:02 | comment | added | Josiah Park | @yarchik Allowing for multiple $\Gamma$'s allows for a positive answer. For instance for $n=3$ if one takes $\Gamma_{i}=e_{i}e_{i}^{T}$, $i=1,\dots,3$ one can recover $A$. | |
| Apr 30, 2019 at 9:01 | comment | added | yarchik | @JosiahPark Indeed $\Gamma=I$ is somewhat a special case. The problem may also be ill posed for $\Gamma$ in the vicinity of $I$. It is my hope, however, solutions may be found for some $\Gamma$. | |
| Apr 30, 2019 at 8:57 | comment | added | yarchik | @user44191 Can you please elaborate about the conjugacy classes? | |
| Apr 30, 2019 at 8:47 | history | edited | Francesco Polizzi |
edited tags
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| Apr 30, 2019 at 8:45 | comment | added | user44191 | If $B$ is a nonsingular matrix that commutes with $\Gamma$, then $B^{-1}AB$ will have the same traces; assuming that $\Gamma$ has distinct eigenvalues, these $B$ are arbitrary diagonal matrices. It may still be possible to determine the $C_G(\Gamma)$-conjugacy class $A$ belongs to in $\mathbb{M}_n$ (though I haven't checked fully). | |
| Apr 30, 2019 at 8:45 | comment | added | Josiah Park | It is not true for $\Gamma=I$. Since $Tr(A^k)=\sum\limits_{i=1}^n \lambda_{i}^k$, no additional information can be retrieved besides the eigenvalues (which are already given). | |
| Apr 30, 2019 at 8:45 | answer | added | Francesco Polizzi | timeline score: 5 | |
| Apr 30, 2019 at 8:11 | history | asked | yarchik | CC BY-SA 4.0 |