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Sign-central matrices

Authors
Journal
Linear Algebra and its Applications
0024-3795
Publisher
Elsevier
Publication Date
Identifiers
DOI: 10.1016/0024-3795(94)90444-8
Disciplines
  • Mathematics

Abstract

Abstract We investigate real matrices A such that each matrix with the same sign pattern as A has a nonzero, nonnegative vector in its nullspace. For geometric reasons we call these matrices sign-central. These matrices were introduced and given a combinatorial characterization by Davydov and Davydova. We give an alternative proof of their characterization. We show that under a minimality assumption a sign-central matrix with m nonzero rows has at least m + 1 columns, and that equality holds if and only if the matrix is an S-matrix (as defined in the theory of sign-solvability).

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