A note on matrices mapping a positive vector onto its element-wise inverse

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:463

Article

Labbe, Sebastien¹ 

[1] CNRS, LaBRI, UMR 5800, F-33400 Talence, France

关键词: Primitive matrices;    Stochastic matrices;    Fixed-point theorems;    Perron theorem;   

DOI  :  10.1016/j.jmaa.2018.03.016

来源: Elsevier

【 摘 要 】

For any primitive matrix M is an element of R-n (x) (n) with positive diagonal entries, we prove the existence and uniqueness of a positive vector x = (x(1,) ..., x(n))(t) such that Mx = (1/x(1), ..., 1/x(n))(t). The contribution of this note is to provide an alternative proof of a result of Brualdi et al. (1966) [1] on the diagonal equivalence of a nonnegative matrix to a stochastic matrix. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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