Existence and construction of nonnegative matrices with prescribed spectrum

We consider the following inverse spectrum problem for nonnegative matrices: given a set of real 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. In particular, by the use of a relevant theorem of Brauer we obtain new simple sufficient conditions for the problem to have a solution. Moreover, we can always construct a solution matrix, which is nonnegative generalized stochastic. (C) 2003 Elsevier Science Inc. All rights reserved.