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Interval hulls of N-matrices and almost P-matrices

Choudhury, PN and Kannan, MR (2021) Interval hulls of N-matrices and almost P-matrices. In: Linear Algebra and Its Applications, 617 . pp. 27-38.

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Official URL: https://dx.doi.org/10.1016/j.laa.2021.01.005


We establish a characterization of almost P-matrices via a sign non-reversal property. In this we are inspired by the analogous results for N-matrices. Next, the interval hull of two m�n matrices A=(aij) and B=(bij), denoted by I(A,B), is the collection of all matrices C�Rn�n such that each cij is a convex combination of aij and bij. Using the sign non-reversal property, we identify a finite subset of I(A,B) that determines if all matrices in I(A,B) are N-matrices/almost P-matrices. This provides a test for an entire class of matrices simultaneously to be N-matrices/almost P-matrices. We also establish analogous results for semipositive and minimally semipositive matrices. These characterizations may be considered similar in spirit to that of P-matrices by Bia�as�Garloff 1 and Rohn�Rex 16, and of positive definite matrices by Rohn 15. © 2021 Elsevier Inc.

Item Type: Journal Article
Publication: Linear Algebra and Its Applications
Publisher: Elsevier Inc.
Additional Information: The copyright of this article belongs to Elsevier Inc.
Keywords: Mathematical techniques, Convex combinations; Finite subsets; Interval hull; P-matrices; Positive-definite matrices, Linear algebra
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 25 Feb 2021 09:14
Last Modified: 25 Feb 2021 09:14
URI: http://eprints.iisc.ac.in/id/eprint/67918

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