Polynomials that preserve nonnegative matrices of order two

Published in Ball State Undergraduate Mathematics Exchange, 2022

Abstract: A known characterization for entire functions that preserve all nonnegative matrices of order two is shown to characterize polynomials that preserve nonnegative matrices of order two. Equivalent conditions are derived and used to prove that P3 ⊂ P2, which was previously unknown. A new characterization is given for polynomials that preserve nonnegative circulant matrices of order two.

Keywords: Polynomial; Nonnegative matrix; Nonnegative inverse eigenvalue problem;