Anthony Cronin

The Diagonalizable Nonnegative Inverse Eigenvalue Problem

Abstract In this articlewe provide some lists of real numberswhich can be realized as the spectra of nonnegative diagonalizable matrices but which are not the spectra of nonnegative symmetric matrices. In particular, we examine the classical list σ = (3 + t, 3 − t, −2, −2, −2) with t ≥ 0, and show that 0 is realizable by a nonnegative diagonalizable matrix only for t ≥ 1. We also provide examples of lists which are realizable as the spectra of nonnegative matrices, but not as the spectra of nonnegative diagonalizable matrices by examining the Jordan Normal Form

Constructive methods for spectra with three nonzero elements in the nonnegative inverse eigenvalue problem

We present and compare three constructive methods for realizing nonreal spectra with three nonzero elements in the nonnegative inverse eigenvalue problem. We also provide some necessary conditions for realizability and numerical examples. In particular, we utilize the companion matrix.