Inertia of Kwong matrices

2023/07/29 by Rajendra Bhatia, Bhatia, Rajendra, Tanvi Jain +1
Computer Science · Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2307.16007

openalex publication_date 2023/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let r be any real number and for any n let p₁,…,p_n be distinct positive numbers. A Kwong matrix is the n× n matrix whose (i,j) entry is (p_i^r+p_j^r)/(p_i+p_j). We determine the signatures of eigenvalues of all such matrices. The corresponding problem for the family of Loewner matrices \beginbmatrix(p_i^r-p_j^r)/(p_i-p_j)\endbmatrix has been solved earlier.

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