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Sums of nilpotent matrices |
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| Authors: | Simion Breaz Grigore Călugăreanu |
| Affiliation: | 1. Deptartment of Mathematics, Babe? -Bolyai University, Cluj-Napoca, Romania.bodo@math.ubbcluj.ro;3. Deptartment of Mathematics, Babe? -Bolyai University, Cluj-Napoca, Romania. |
| Abstract: | We study matrices over general rings which are sums of nilpotent matrices. We show that over commutative rings all matrices with nilpotent trace are sums of three nilpotent matrices. We characterize 2-by-2 matrices with integer entries which are sums of two nilpotents via the solvability of a quadratic Diophantine equation. Some exemples in the case of matrices over noncommutative rings are given. |
| Keywords: | Nilpotent matrix trace quadratic Diophantine equation commutator |