Construction of nonnegative symmetric matrices with given spectrum

Let sigma = (lambda(1),..., lambda(n)) be the spectrum of a nonnegative symmetric matrix A with the Perron eigenvalue lambda(1), a diagonal entry c and let tau = (mu(1),..., mu(m)) be the spectrum of a nonnegative symmetric matrix B with the Perron eigenvalue mu(1). We show how to construct a nonnegative symmetric rnatrix C with the spectrum (lambda(1) + max{0, mu(1) - c}, lambda(2), . . . , lambda(n), mu(2), . . . , mu(m)). (c) 2006 Elsevier Inc. All rights reserved.