A note concerning the invertibility of certain alternant matrices

TL;DR

This paper investigates the conditions under which specific alternant matrices, composed of polynomials and their logarithmic products, are invertible, providing insights into their mathematical properties.

Contribution

It establishes criteria for the invertibility of certain alternant matrices involving polynomials and logarithms, extending previous understanding.

Findings

Alternant matrices with polynomial and logarithmic entries can be invertible under specific degree conditions.

The paper provides mathematical conditions ensuring invertibility.

Results contribute to the theory of polynomial and logarithmic matrix structures.

Abstract

This brief note concerns the invertibility of certain alternant matrices. In particular those that consisting of polynomials and products of polynomials and logarithms are shown to be invertible under appropriate conditions on the degrees of the polynomials.