Products of EP matrices

Necessary and sufficient conditions are given for a matrix to be a product of an EP_r matrix by an EP_s matrix. It is shown that a given square matrix is a product of more than two EP matrices of specified ranks (and hence nullities) if and only if its rank is less than or equal to the minimum of the given ranks and its nullity is less than or equal to the sum of the given nullities. It is also shown that given two EP matrices, the rank of their product is independent of the order of the factors.