In minisymposium: Combinatorial Matrix TheoryThu 17:30–18:00, Room AV 04.17
The longstanding nonnegative inverse eigenvalue problem (RNIEP) is to determine which sets of real numbers occur as the spectra of entrywise nonnegative matrices. Recently , 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.
- C. R. Johnson and P. Paparella, Perron spectratopes and the real nonnegative inverse eigenvalue problem, Linear Algebra Appl. 493 (2016), pp. 281–300.