Perron–Frobenius theorem for matrices with some negative entries Original Research Article

We extend the classical Perron–Frobenius theorem to matrices with some negative entries. We study the cone of matrices that has the matrix of 1ʹs (eet) 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 eet that guarantees this property.