The inverse eigenvalue problem for nonnegative matrices

Abstract Let A be a nonnegative matrix with spectrum ( λ 1 , λ 2 ,…, λ m ) and B be a nonnegative matrix with spectrum ( μ 1 , μ 2 ,…, μ n ), where μ 1 is the Perron eigenvalue of B . Furthermore, let a maximal diagonal element of A be greater than or equal to μ 1 . In the article we construct a nonnegative matrix C with spectrum ( λ 1 , λ 2 ,…, λ m , μ 2 ,…, μ n ). This construction enables us to obtain several results on how to determine new realizable lists from known realizable lists.