PERRON-FROBENIUS THEORY ON THE NUMERICAL RANGE FOR SOME CLASSES OF REAL MATRICES

We give further results for Perron-Frobenius theory on the numerical range of real matrices and some other results generalized from nonnegative matri- ces to real matrices. We present an extension of Perron-Frobenius theory to the spectrum and the numerical range of real matrices. We indicate two techniques for establishing the main theorem of Perron and Frobenius on the numerical range. In the rst method, we use a corresponding version of Wielandt s lemma. The second technique involves graph theory.