Timeline for Decomposition of Matrices in Semisimple and Nilpotent Parts
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 1, 2015 at 19:06 | comment | added | LSpice | @grp, what is the definition of semisimplicity that is distinct from geometric semisimplicity? (For those who learned the Jordan decomposition from Borel, they are the same by definition.) Is it that the minimal polynomial is irreducible over $k$? | |
| Oct 3, 2012 at 21:57 | vote | accept | Miguel | ||
| Oct 1, 2012 at 11:23 | comment | added | grp | The example in #3 (which readily adapts to any imperfect field $k$ using the $k$-linear multiplication by $a^{1/p}$ on $V = k(a^{1/p})$) isn't an entirely satisfactory counterexample because it is semisimple over $k$ (though not "geometrically semisimple"; i.e., not diagonalizable over $\overline{k}$). The Wikipedia entry has now been updated to give an example over any imperfect field $k$ in which the operator isn't a sum of two commuting $k$-linear operators that are respectively semisimple (just over $k$!) and nilpotent. | |
| Sep 29, 2012 at 15:58 | comment | added | Anton Klyachko | We should demand that $R$ and $M$ commute. | |
| Sep 29, 2012 at 15:17 | history | edited | Laurent Berger | CC BY-SA 3.0 |
added 82 characters in body
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| Sep 29, 2012 at 14:27 | history | answered | Laurent Berger | CC BY-SA 3.0 |