关于非负矩阵优势比的界

令A为一n×n复矩阵,且令这个比率d称为矩阵A的优势比.1964年,Ostrowski得到正矩阵优势比的一个界.1974年,Ostrowski又得到既约非负矩阵优势比的一个界. 在本文中,我们得一个比4]更好的界,我们的结果还推广到类似于既约非负矩阵的另一类矩阵,即在1]中定义的准非负矩阵.此外,我们还给出确定本原指标v(A)的一个简单方法,这样可以得到优势比的更佳界.

ON THE BOUND FOR DOMINANCE RADIO OF NONNEGATIVE MATRICES

Let A be an n×n complex matrix, and let The radio d is called dominance ratio of matrix A. In 1964, A. M. Ostrowski 3] obtained a bound for dominance radio of positive matrices. In 1974, Ostrowski 4] also obtained a bound for dominance radio of irreducible nonnegative matrices.In this paper we have obtained a bound better than that of Ostrowski 4]. Our result is further extended to some other types of matrices such as irreducible nonnegative matrices, namely, sub-nonnegative matrices defined in our paper 1]. In addition, we also give a simple methodto determine primitive character γ(A) (in the sense that for A ≥ 0, γ(A) = min{K|A~k > 0}, where k is a positive integer). Thus better bounds for dominance radio may be obtained.