Abstract

The following inverse spectrum problem for nonnegative matrices is considered: given a set of complex numbers ? = {?1, ?2,..., ?n}, find necessary and sufficient conditions for the existence of an n × n nonnegative matrix A with spectrum ?. 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 ?0 ? max2?j?n |?j| such that the problem has a solution if and only if ?1 ? ?0. In particular, we discuss how to compute ?0 and the solution matrix A for certain class of matrices. A sufficient condition for the problem to have a solution is also derived. © 2003 Elsevier Science Inc. All rights reserved.