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.
- © 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