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May 4, 2020 at 12:54 comment added Mikko Korhonen The answer is positive over any algebraically closed field. See the following question at math.stackexchange: link.
Jan 24, 2020 at 15:46 comment added Eric Wofsey You're right, and apparently it took over 10 years for anyone to catch that! I've corrected the argument at the end.
Jan 24, 2020 at 15:45 history edited Eric Wofsey CC BY-SA 4.0
added 494 characters in body
Jan 24, 2020 at 14:48 comment added Zach Teitler Well, just to nitpick a bit, there are some minor wrinkles, like if $T\begin{pmatrix} a & b \\ c & d \end{pmatrix}= \begin{pmatrix} a & -b \\ -c & d \end{pmatrix}$. Then we would have to change $T$ one more time by conjugating with $\operatorname{diag}(1,-1)$ or similar.
Oct 12, 2015 at 17:40 history edited Eric Wofsey CC BY-SA 3.0
texify and minor corrections
Oct 15, 2009 at 0:57 history edited Eric Wofsey CC BY-SA 2.5
deleted 153 characters in body
Oct 15, 2009 at 0:30 history answered Eric Wofsey CC BY-SA 2.5