Power Series with Positive Coefficients in the Context of the Nonnegative Inverse Eigenvalue Problem

Speaker: Helena Smigoc (UCD)

Time: 4.00 PM

Date: Monday 24th September 2012

Location: Casl Seminar Room (Belfield Office Park)


Let f(t)=det(I-tA), where A is an (entrywise) positive matrix. We show that there always exists a positive integer N such that the power series expansion of (1-f(t))^{1/N} around zero has positive coefficients. We will explain how this result arose from the study of the nonnegative inverse eigenvalue problem: finding necessary and sufficient conditions for a list of complex numbers to be the spectrum of a nonnegative matrix. The talk is based on a joint work with Thomas J. Laffey and Raphael Loewy.

Series: Algebra Seminar Series