Power series with positive coefficients arising from the characteristic polynomials of positive matrices

TL;DR

This paper proves that for any positive matrix, the characteristic polynomial's related power series can be transformed into a form with positive coefficients, revealing new positivity properties of matrix determinants.

Contribution

It introduces a novel positivity result for power series derived from the characteristic polynomial of positive matrices, expanding understanding of matrix spectral properties.

Findings

Existence of an integer N making 1 - f(t)^{1/N} have positive coefficients

Establishment of positivity properties for power series from positive matrices

Insights into the structure of characteristic polynomials of positive matrices

Abstract

Let A be an nxn (entrywise) positive matrix and let f(t)=det(I-t A). We prove that there always exists a positive integer N such that 1-f(t)^{1/N} has positive coefficients.