Eigenvalue location for nonnegative and Z-matrices

AbstractLet Lk0 denote the class of n × n Z-matrices A = tl − B with B ⩾ 0 and ϱk(B) ⩽ t < ϱk + 1(B), where ϱk(B) denotes the maximum spectral radius of k × k principal submatrices of B. Bounds are determined on the number of eigenvalues with positive real parts for A ϵ Lk0, where k satisfies, ⌊n2⌋ ⩽ k ⩽ n − 1. For these classes, when k = n − 1 and n − 2, wedges are identified that contain only the unqiue negative eigenvalue of A. These results lead to new eigenvalue location regions for nonnegative matrices