Some spectral properties of an operator associated with a pair of nonnegative matrices
M. V. Menon · Transactions of the American Mathematical Society · 1968
An operator—in general nonlinear—associated with a pair of non-negative matrices, is defined and some of its spectral properties studied. If the pair of matrices are a square matrix A and the identity matrix of the same order, the operator reduces to the linear operator A . The results obtained include generalizations of one of the principal conclusions of the theorem of Perron-Frobenius.