Perron–Frobenius theorem for matrices with some negative entries

Abstract We extend the classical Perron–Frobenius theorem to matrices with some negative entries. We study the cone of matrices that has the matrix of 1's ( ee t ) as the central ray, and such that any matrix inside the cone possesses a Perron–Frobenius eigenpair. We also find the maximum angle of any matrix with ee t that guarantees this property.