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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Matrix commutators over an algebraically closed field
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by P. M. Gibson PDF
Proc. Amer. Math. Soc. 52 (1975), 30-32 Request permission

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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Additional Information
  • © Copyright 1975 American Mathematical Society
  • 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