A note on matrix solutions to $A=XY-YX$

Abstract

Abstract.It is known that a square matrix A can be written as a commutator XY-YX'xi and only if Tr(/1)=0. In this note it is shown further that for a fixed A the spectrum of one of the factors may be taken to be arbitrary while the spectrum of the other factor is arbitrary as long as the characteristic roots are distinct. The distinctness restriction on one of the factors may not in general be relaxed.