Intervals of certain classes of Z-matrices

M. Kannan; K. Sivakumar

ArticleOriginal scientific text

Title

Intervals of certain classes of Z-matrices

Authors ¹, ¹

Affiliations

Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India

Abstract

Let A and B be M-matrices satisfying A ≤ B and J = [A,B] be the set of all matrices C such that A ≤ C ≤ B, where the order is component wise. It is rather well known that if A is an M-matrix and B is an invertible M-matrix and A ≤ B, then aA + bB is an invertible M-matrix for all a,b > 0. In this article, we present an elementary proof of a stronger version of this result and study corresponding results for certain other classes as well.

Keywords

ENG

interval matrix, M-matrix, N-matrix, N₀-matrix, nonnegativity

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Title

Intervals of certain classes of Z-matrices

Affiliations

Abstract

Keywords

Bibliography