Products of idempotent and square-zero matrices

This paper presents necessary and sufficient conditions for a square matrix over an arbitrary field to be expressed as a product of idempotent and square-zero matrices. Since the similarity structures of such factors are completely determined by their rank, we also investigate the ranks that these factors may have. The case where the factors are all idempotent or all square-zero have been investigated by various authors, some of whom are listed in the references of this paper.