publication . Preprint . 2018

Perron-Frobenius Theorem for Rectangular Tensors and Directed Hypergraphs

Lu, Linyuan; Yang, Arthur L. B.; Zhao, James J. Y.;
Open Access English
  • Published: 23 Apr 2018
Comment: 1. One of the main results "Theorem 3.2" has already been proved under a more general setting by Antoine Gautier and Francesco Tudisco in the paper arXiv:1801.04215. 2. Example 2.1 contains an error; the strong eigenvalue-eigenvectors triple actually exists
free text keywords: Mathematics - Combinatorics, 15A18, 15A69, 05C65
Download from
25 references, page 1 of 2

[1] M. Akian, S. Gaubert and R. Nussbaum, Uniqueness of the fixed point of nonexpansive semidifferentiable maps, Trans. Amer. Math. Soc. 368(2) (2016), 1271-1320.

[2] S. Bai and L. Lu, Spectral Radius of {0,1}-tensor with prescribed number of ones, arXiv:1801.02784.

[4] E.F. Beckenbach and R. Bellman, Inequalities, Springer-Verlag, Berlin, 1961.

[5] K.C. Chang, K. Pearson, and T. Zhang, Perron-Frobenius theorem for nonnegative tensors, Commun. Math. Sci. 6(2) (2008), 507-520.

[6] J. Cooper and A. Dutle, Spectra of uniform hypergraphs, Linear Algebra Appl. 436 (2012), 3268- 3292.

[7] P. Etingof, D. Nikshych, and V. Ostrik, On fusion categories, Ann. Math. 162(2) (2005), 581-642.

[8] S. Friedland, S. Gaubert, and L. Han, Perron-Frobenius theorem for nonnegative multilinear forms and extensions, Linear Algebra Appl. 438(2) (2013), 738-749.

[9] G. Frobenius, Ueber Matrizen aus nicht negativen Elementen, Sitzungsber. K¨onigl. Preuss. Akad. Wiss. (1912), 456-477.

[10] S. Gaubert and J. Gunawardena, The Perron-Frobenius theorem for homogeneous, monotone functions, Trans. Amer. Math. Soc. 356 (2004), 4931-4950. [OpenAIRE]

[11] L.P. Hansen and J.A. Scheinkman, Long-term risk: An operator approach, Econometrica 77(1) (2009), 177-234.

[12] L.P. Hansen and J.A. Scheinkman, Recursive utility in a Markov environment with stochastic growth, Proc. Natl. Acad. Sci. USA 109(30) (2012), 11967-11972.

[13] J.P. Keener, The Perron-Frobenius theorem and the ranking of football teams, SIAM Review 35(1) (1993), 80-93. [OpenAIRE]

[14] Y.-I. Kim and X. Yang, Generalizations and refinements of Ho¨lders inequality, Appl. Math. Lett. 25 (2012), 1094-1097.

[15] A.N. Langville and C.D. Meyer, Google's PageRank and Beyond: The Science of Search Engine Rankings, Princeton University Press, Princeton and Oxford (2012).

[16] R. Larson and D. Radford, Semisimple cosemisimple Hopf algebras, Amer. J. Math. 110(1) (1988), 187-195. [OpenAIRE]

25 references, page 1 of 2
Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue