A Survey of M-Matrix Characterizations. I. Nonsingular M-Matrices.

Abstract

The purpose of this survey is to classify systematically a widely ranging list of characterizations of nonsingular M-matrices from the economics and mathematics literatures. These characterizations are grouped together in terms of their relationships to the properties of (1) positivity of principal minors (2) inverse-positivity and splittings (3) stability and (4) semi-positivity and diagonal dominance. A list of forty eqivalent conditions is given for a square matrix A with nonpositive off-diagonal entries to be a nonsingular M-matrix. These conditions are grouped into classes in order to identify those that are equivalent for arbitrary real matrices A. In addition, other remarks relating nonsingular M-matrices to certain complex matrices are made and the recent literature on these general topics is surveyed. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1976
Accession Number
ADA031963

Entities

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  • R. J. Plemmons

Organizations

  • University of Wisconsin–Madison

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  • Mathematics

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