Work

Constructing strictly sign regular matrices of all sizes and sign patterns

Year: 2025

Type: article

Abstract: The class of strictly sign regular (SSR) matrices has been extensively studied by many authors over the past century, notably by Schoenberg, Motzkin, Gantmacher, and Krein. A classical result of Gantmacher–Krein assures the existence of SSR matrices for any dimension and sign pattern. In this article, we provide an algorithm to explicitly construct an SSR matrix of any given size and sign pattern. (We also provide in the Appendix, a Python code implementing our algorithm.) To develop this algorithm, we show that one can extend an SSR matrix by adding an extra row (column) to its border, resulting in a higher order SSR matrix. Furthermore, we show how inserting a suitable new row/column between any two successive rows/columns of an SSR matrix results in a matrix that remains SSR. We also establish analogous results for SSR matrices of order for any .

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70080

Authors: Projesh Nath Choudhury, Shivangi Yadav

Institution: Indian Institute of Technology Gandhinagar

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Indian Institute of Technology Gandhinagar, Department of Science and Technology, Ministry of Science and Technology, India

Awards: G4439361554, G5028385064