广义长方形张量的注记

(1.新疆师范大学数学科学学院,新疆 乌鲁木齐 830054; 2.新疆大学数学科学学院,新疆 乌鲁木齐 830046)

特征值; 三维长方形张量; 不可约; Perron-Frobenius定理

A Note on Generalized Rectangular Tensor
LIU Bingjie1,BIAN Hong1*,YU Haizheng2,MA Li1

(1.School of Mathematical Sciences,Xinjiang Normal University,Urumqi 830054,China; 2.College of Mathematics and System Sciences,Xinjiang University,Urumqi 830046,China)

eigenvalue; three dimensional rectangular tensor; irreducible; Perron-Frobenius theorem

DOI: 10.6043/j.issn.0438-0479.201603001

备注

Perron-Frobenius 定理是非负矩阵的基本结果.特别地,非负张量的 Perron-Frobenius 定理与测量链接对象的高阶连通性和超图有关.在长方形张量的基础上定义一个广义长方形张量,并给出了非负广义长方形张量的 Perron-Frobenius定理的一些新的结果.

The Perron-Frobenius theorem is a fundamental result for nonnegative matrices.In particular,the Perron-Frobenius theorem for nonnegative tensors is related to measuring higher order connectivity in linked objects and hypergraphs.In this paper,we define a generalized rectangular tensor which is based on the definition of rectangular tensors,and give some new results on the Perron-Frobenius theorem for nonnegative generalized rectangular tensor.