The inverse eigenvalue problem for 6x6 nonnegative symmetric matrices

Abstract

The symmetric nonnegative inverse eigenvalue problem is to determine when a set of n real numbers is the spectrum of an n x n symmetric nonnegative matrix. In particular, necessary and sufficient conditions are sought. For n less than or equal to 4, the inverse eigenvalue problem for nonnegative symmetric matrices is completely solved. However, the problem still open for n = 5 and above. Our purpose is to discuss this problem for nonnegative symmetric matrices of order n = 6.