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)

**Abstract:**

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**

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