1DEPARTMENT OF MATHEMATICS, HORMOZGAN UNIVERSITY, P. O. BOX 3995, BANDAR ABBAS, IRAN
2DEPARTMENT OF MATHEMATICS, VALI-E-ASR UNIVERSITY OF RAFSANJAN, P. O. BOX 518, RAFSANJAN, IRAN
We give further results for Perron-Frobenius theory on the numerical range of real matrices and some other results generalized from nonnegative matrices to 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.