Perron-Frobenius theory on the higher-rank numerical range for some classes of real matrices

We present an extension of Perron-Frobenius theory to the higherrank numerical rangeof real matrices. We define a new type of the rankk numerical radius for real matrices, i.e., the sign-real rank-k numerical radius‎, and derive some properties of it. In addition, we extend Issos’ results on the higherrank numerical range of nonnegative matrices to real matrices.‎ Finally, we give some examples that are used to illustrate our theoretical results.‎‎