Perron-Frobenius定理的新证明

A NEW PROOF FOR THE PERRON-FROBENIUS THEOREM

本文给出了Perron-Frobenius定理的新证明,获得了M矩阵的一个新性质,并且对非负可约矩阵A,给出了谱半径ρ(A)为单根和重根的充分必要性质。

In this paper, the authors give a new proof for the Perron-Frobenius theorem. A new property of M-matrix is obtained, and for a reducible nonnegative matrix A, a sufficient and necessary condition that ρ(A) is either simple or multiple eigenvalues of matrix A is generated.