A Note on Matrix Solutions to A = XY - YX

Matrix Commutators Over an Algebraically Closed Field

“…Clearly if A has property K then tr(A) = 0. C. R. Johnson [2] proved the converse in the case where F is the complex field. We show that every rc-square nonscalar matrix is similar to a matrix with n-1 zero diagonal entries, and then use this result and a theorem due to S. Friedland [l] to extend Johnson's result to arbitrary algebraically closed fields.…”