H-tensors and nonsingular H-tensors

作     者：Xuezhong WANG Yimin WEI 

作者机构：School of Mathematical Sciences Fudan University Shanghai 200433 China School of Mathematics and Statistics Hexi University Zhangye 734000 China 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2016年第11卷第3期

页      面：557-575页

核心收录：

学科分类：07[理学] 08[工学] 080104[工学-工程力学] 070104[理学-应用数学] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：Acknowledgements The authors would like to thank Professors Liqun Qi and Yiju Wang for their comments and the preprint . They would like to thank two referees for their detailed suggestions which greatly improve the presentation. They also thank Prof. Liqun Qi for kindly reminding them of the very recent paper after their first revision in February  2015. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11171371  11271084.) 

主　　题：Diagonally dominant irreducible diagonally dominant H-tensor,nonsingular 

摘      要：The H-matrices are an important class in the matrix theory, and have many applications. Recently, this concept has been extended to higher order H-tensors. In this paper, we establish important properties of diagonally dominant tensors and H-tensors. Distributions of eigenvalues of nonsingular symmetricH-tensors are given. An J（t%-tensor is semi-positive, which enlarges the area of semi-positive tensor from H-tensor to H＋-tensor. The spectral radius of Jacobi tensor of a nonsingular （resp. singular） H-tensor is less than （resp. equal to） one. In particular, we show that a quasi-diagonally dominant tensor is a nonsingular H-tensor if and only if all of its principal sub-tensors are nonsingular H-tensors. An irreducible tensor H is an H-tensor if and only if it is quasi-diagonally dominant.