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.References
- Shmuel Friedland, Matrices with prescribed off-diagonal elements, Israel J. Math. 11 (1972), 184–189. MR 379526, DOI 10.1007/BF02762620
- Charles R. Johnson, A note on matrix solutions to $A=XY-YX$, Proc. Amer. Math. Soc. 42 (1974), 351–354. MR 332826, DOI 10.1090/S0002-9939-1974-0332826-1
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