Realizable regions for the symmetric nonnegative inverse eigenvalue problem for 6 × 6 matrices

Abstract

The symmetric nonnegative inverse eigenvalue problem is to determine when a multiset of n real numbers is the spectrum of a symmetric nonnegative n × n matrix. The problem is solved only for n ≤ 4 . In this article, the authors examine the set of possible spectra for nonnegative symmetric 6 × 6 matrices, dividing the set into points that are realizable, points that are unrealizable by known necessary conditions, and points that satisfy all known necessary conditions, but their realizability remains unknown.