On the existence of matrices with prescribed height and level characteristics (Q1191994)

The authors obtain necessary and sufficient conditions for the existence of an \(M\)-matrix with the given height (Weyr) and level characteristics; for definitions, see \textit{D. Hershkowitz} and \textit{H. Schneider} [Linear Multilinear Algebra 29, No. 1, 21-42 (1991; Zbl 0759.05021)]. Both characteristics are finite sequences of positive integers, and the necessary and sufficient conditions are that the sequences be of the same length and that the height characteristic majorize (in the sense consistent with the definition in \textit{D. Hershkowitz} and \textit{H. Schneider}, ibid. 25, No. 2, 149-171 (1989; Zbl 0687.15017)] the level characteristic reordered in a non-increasing order. The result conjectured by Berman and van den Driessche in a private communication to the authors, answers a question posed by \textit{H. Schneider} [Linear Algebra Appl. 84, 161-189 (1986; Zbl 0613.15017)].