Existence and construction of nonnegative matrices with complex spectrum

The following inverse spectrum problem for nonnegative matrices is considered: given a set of complex numbers sigma = {lambda(1), lambda(2), ..., lambda(n)}, find necessary and sufficient conditions for the existence of an n x n nonnegative matrix A with spectrum sigma. Our work is motivated by a relevant theoretical result of Guo Wuwen [Linear Algebra Appl. 266 (1997) 261, Theorem 2.1]: there exists a real parameter; lambda(0) greater than or equal to max(2less than or equal tojless than or equal ton)\lambda(j)\ such that the problem has a solution if and only if lambda(1) greater than or equal to lambda(0). In particular, we discuss how to compute lambda(0) and the solution matrix A for certain class of matrices. A sufficient condition for the problem to have a solution is also derived. (C) 2003 Elsevier Science Inc. All rights reserved.