Matrix Commutators Over an Algebraically Closed Field
P. M. Gibson · Proceedings of the American Mathematical Society · 1975
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.