Products of matrices with prescribed nullities and traces (Q676027)

Let \(A\) and \(A_i\) be matrices over a field \(F\). The author gives necessary and sufficient conditions for a matrix \(A\) to be a product of matrices \(A_i\), \(i=1,\dots,k\), where each \(A_i\) has prescribed trace. If \(A\) is a singular matrix, then factorizations are considered, where for each \(A_i\) the nullity and the trace are prescribed. The results are applied to write \(A\) as a product of additive commutators.