Eigenvalue location for nonnegative and Z-matrices Original Research Article

Let Lk0 denote the class of n × n Z-matrices A = tl − B with B greater-or-equal, slanted 0 and varrhok(B) less-than-or-equals, slant t < varrhok + 1(B), where varrhok(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, left floorn/2right floor less-than-or-equals, slant k less-than-or-equals, slant 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.