Perron-Frobenius Properties of General Matrices
نویسندگان
چکیده
A matrix is said to have the Perron-Frobenius property if it has a positive dominant eigenvalue that corresponds to a nonnegative eigenvector. Matrices having this and similar properties are studied in this paper. Characterizations of collections of such matrices are given in terms of the spectral projector. Some combinatorial, spectral, and topological properties of such matrices are presented, and the similarity transformations preserving the Perron-Frobenius property are completely described. In addition, certain results associated with nonnegative matrices are extended to matrices having the Perron-Frobenius property.
منابع مشابه
PERRON-FROBENIUS THEORY ON THE NUMERICAL RANGE FOR SOME CLASSES OF REAL MATRICES
We give further results for Perron-Frobenius theory on the numericalrange of real matrices and some other results generalized from nonnegative matricesto real matrices. We indicate two techniques for establishing the main theorem ofPerron and Frobenius on the numerical range. In the rst method, we use acorresponding version of Wielandt's lemma. The second technique involves graphtheory.
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