On a question of Bhatia, Friedland and Jain. Issue 16 (10th December 2021)

• Record Type: Journal Article
• Authors: Kapil, Yogesh; Kaur, Rupinderjit; Singh, Mandeep
• Is Part Of: Linear & multilinear algebra. Volume 69:Issue 16(2021)
• Page Start: 3031
• Page End: 3042
• Publication Date: 2021-12-10
• Subjects: Loewner matrix -- Vandermonde matrix -- schur polynomials -- Littlewood–Richardson coefficients; Primary 15A15 -- 05E05; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2019.1704210
• Languages: English
• ISSNs: 0308-1087

Abstract

ABSTRACT: Let p 1 < p 2 < ⋯ < p n be positive numbers, then for any integer m the Loewner matrix associated with the function x m is given by L m = ( p i m − p j m ) / ( p i − p j ) i, j = 1 n . A question was left open in a paper [Bhatia R, Friedland S, Jain T. Inertia of loewner matrices. Indiana Univ Math J. 2016;65:1251–1261] by Bhatia, Friedland and Jain to find formulas for the determinants of the matrices L m in the case n = 3. We aim to answer this question firmly in terms of the Schur polynomials in this paper.