ILAS2016 — 11–15 July 2016 — KU Leuven, Belgium

20th Conference of the International Linear Algebra Society (ILAS)

20th ILAS Conference

In minisymposium: Combinatorial Matrix Theory

Thu 17:30–18:00, Room AV 04.17
Perron Spectratopes and the Real Nonnegative Inverse Eigenvalue Problem
Pietro Paparella (University of Washington Bothell)
Joint work with Charles R. Johnson (The College of William & Mary)

The longstanding nonnegative inverse eigenvalue problem (RNIEP) is to determine which sets of real numbers occur as the spectra of entrywise nonnegative matrices. Recently [1], Charles R. Johnson and I introduced the (Perron) spectratope and (Perron) spectracone to investigate the RNIEP (and several of its variants, most notably, the symmetric NIEP). In this talk I will provide an overview of spectratopes and spectracones, state recent results, discuss the role of permutative matrices, and implications for future research.

  1. C. R. Johnson and P. Paparella, Perron spectratopes and the real nonnegative inverse eigenvalue problem, Linear Algebra Appl. 493 (2016), pp. 281–300.