Nonnegatively realizable spectra with two positive eigenvalues

摘要

Boyle and Handelman [M. Boyle and D. Handelman, The spectra of nonnegative matrices via symbolic dynamics, Ann. Math. 133 (1991), pp. 249-316.] characterized all lists of n complex numbers that can be the nonzero spectrum of a nonnegative matrix. This article presents a constructive proof of this result in the special case when the lists are real and contain two positive numbers and n − 2 negative numbers. A bound for the number of zeros that needs to be added to the list to achieve a nonnegative realization is presented in this case.