On the existence of matrices with prescribed height and level characteristics
type: Item
instance of: scholarly article
title: On the existence of matrices with prescribed height and level characteristics
zbMATH Open document ID: 0798.15026
DOI: 10.1007/BF02787184
author: Daniel Hershkowitz
author: Hans Schneider
published in: Israel Journal of Mathematics
publication date: 1992-09-27T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 63273
zbMATH Keywords: height (Weyr) characteristic
zbMATH Keywords: level characteristic
zbMATH Keywords: \(M\)-matrix
reviewed by: Mark Kleiner
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02787184
OpenAlex ID: W2128847348
description: scientific article; zbMATH DE number 63273