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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Matrix commutators over an algebraically closed field


Author: P. M. Gibson
Journal: Proc. Amer. Math. Soc. 52 (1975), 30-32
MSC: Primary 15A24
DOI: https://doi.org/10.1090/S0002-9939-1975-0412207-3
MathSciNet review: 0412207
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Abstract: Let $A$ be an $n$-square matrix with zero trace over an algebraically closed field $F$, and let the characteristic of $F$ not divide $n$. It is shown that $A$ can be expressed as $A = XY - YX$ where the eigenvalues of $X$ and $Y$ may be arbitrarily specified as long as those of $X$ are distinct.


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Article copyright: © Copyright 1975 American Mathematical Society