More on generalizations of matrix monotonicity |
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| Authors: | Michael Neumann George D Poole Hans Joachim Werner |
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| Institution: | Department of Mathematics and Statistics University of South Carolina Columbia, South Carolina 29208 USA;Department of Mathematics Emporia State University Emporia, Kansas 66801 USA;Institute for Econometrics and Operations Research Econometrics Unit University of Bonn Adenauerallee 24-42 D-5300 Bonn 1, West Germany |
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| Abstract: | Following Berman and Plemmons 5], Werner 17], Poole and Barker 13], and others, we investigate some generalizations of matrix monotonicity and consider their relation to MP matrices. We prove some observations on almost monotone, MP, and group monotone matrices. However, of much interest to us is the problem whether a symmetric positive semidefinite matrix is MP if and only if it is monotone on its range. To consider this question we obtain several results on the structure of range monotone matrices. |
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