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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
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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DOI: https://doi.org/10.1090/S0002-9939-1975-0412207-3
Article copyright: © Copyright 1975 American Mathematical Society