Nonnegative Inverse Elementary Divisors Problem for Lists with Nonnegative Real Parts

Abstract

In this paper, sufficient conditions for the existence and construction of nonnegative matrices with prescribed elementary divisors for a list of complex numbers with nonnegative real part are obtained, and the corresponding nonnegative matrices are constructed. In addition, results of how to perturb complex eigenvalues of a nonnegative matrix while keeping its elementary divisors and its nonnegativity are derived.

Keywords

• nonnegative inverse elementary divisors problem
• nonnegative matrices
• Jordan canonical form