Characterizations of the spectral radius of nonnegative weakly irreducible tensors via a digraph

被引：6

作者：

Sun, Lizhu ^{[1
]}

Zheng, Baodong ^{[1
]}

Wei, Yimin ^{[2
]}

Bu, Changjiang ^{[3
]}

机构：

[1] Harbin Inst Technol, Sch Sci, Harbin 150006, Peoples R China

[2] Fudan Univ, Shanghai Key Lab Contemporary Appl Math, Sch Math Sci, Shanghai 200433, Peoples R China

[3] Harbin Engn Univ, Coll Automat, Coll Sci, Harbin, Peoples R China

来源：

LINEAR & MULTILINEAR ALGEBRA | 2016年 / 64卷 / 04期

基金：

中国国家自然科学基金;

关键词：

nonnegative tensor; spectral radius; digraph; k-uniform hypergraph; PERRON-FROBENIUS THEOREM; EIGENVALUES;

D O I：

10.1080/03081087.2015.1120702

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a nonnegative weakly irreducible tensor A, we give some characterizations of the spectral radius of A, by using the digraph associated with the tensor A. As applications, some bounds on the spectral radius of the adjacency tensor and the signless Laplacian tensor of a k-uniform hypergraph are obtained.

引用

页码：737 / 744

页数：8

共 18 条

[1]

[Anonymous], 1982, Linear and Multilinear Algebra

[2]

Brualdi R.A., 1991, ENCY MATH ITS APPL, V39

[3]

Bu C, FRONT MATH CHINA

[4] Brualdi-type eigenvalue inclusion sets of tensors [J].

Bu, Changjiang ;

Wei, Yuanpeng ;

Sun, Lizhu ;

Zhou, Jiang .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 480 :168-175

[5]

Chang KC, 2008, COMMUN MATH SCI, V6, P507

[6] PRIMITIVITY, THE CONVERGENCE OF THE NQZ METHOD, AND THE LARGEST EIGENVALUE FOR NONNEGATIVE TENSORS [J].

Chang, Kung-Ching ;

Pearson, Kelly J. ;

Zhang, Tan .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2011, 32 (03) :806-819

[7] Spectra of uniform hypergraphs [J].

Cooper, Joshua ;

Dutle, Aaron .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2012, 436 (09) :3268-3292

[8] Perron-Frobenius theorem for nonnegative multilinear forms and extensions [J].

Friedland, S. ;

Gaubert, S. ;

Han, L. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2013, 438 (02) :738-749

[9] The largest Laplacian and signless Laplacian H-eigenvalues of a uniform hypergraph [J].

Hu, Shenglong ;

Qi, Liqun ;

Xie, Jinshan .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 469 :1-27

[10] The Laplacian of a uniform hypergraph [J].

Hu, Shenglong ;

Qi, Liqun .

JOURNAL OF COMBINATORIAL OPTIMIZATION, 2015, 29 (02) :331-366

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