Sums of two square-zero matrices over an arbitrary field

Abstract: The problem to express an matrix A as the sum of two square-zero matrices was first investigated by Wang and Wu for matrices over the complex field. This paper investigates the problem over an arbitrary field F. It is shown that, if char, then is the sum of two square-zero matrices if and only if A is similar to a matrix of the form , where N is nilpotent, X is nonsingular, and each is a companion matrix associated with an even-power poly nomial with nonzero constant term. If F is of characteristic two, the term falls away. If F is of characteristic zero and algebraically closed, the term falls away and the result of Wang and Wu is obtained. [Copyright &y& Elsevier]