Some results on l^k-eigenvalues of tensor and related spectral radius

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2011, 1(3): 381-388. doi: 10.3934/naco.2011.1.381

Some results on $l^k$-eigenvalues of tensor and related spectral radius

1.	School of Science, Hangzhou Dianzi University, Hangzhou, 310018, China
2.	Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong

Received April 2011 Revised July 2011 Published September 2011

Abstract
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In this paper, we study the $l^k$-eigenvalues/vectors of a real symmetric square tensor. Specially, we investigate some properties on the related $l^k$-spectral radius of a real nonnegative symmetric square tensor.

Keywords: $l^k$-eigenvalue, irreducibility., $l^k$-spectral radius, Nonnegative tensor.

Mathematics Subject Classification: Primary: 15A18, 15A69; Secondary: 90C3.

Citation: Chen Ling, Liqun Qi. Some results on $l^k$-eigenvalues of tensor and related spectral radius. Numerical Algebra, Control & Optimization, 2011, 1 (3) : 381-388. doi: 10.3934/naco.2011.1.381

References:

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References:

[1]	L. Bloy and R. Verma, On computing the underlying fiber directions from the diffusion orientation distribution function,, in, (2008), 1. Google Scholar
[2]	K. C. Chang, K. Pearson and T. Zhang, Perron Frobenius theorem for nonnegative tensors,, Commu Math Sci, 6 (2008), 507. Google Scholar
[3]	K. C. Chang, L. Qi and G. Zhou, Singular values of a real rectangular tensor,, J. Math. Anal. Appl., 370 (2010), 284. doi: 10.1016/j.jmaa.2010.04.037. Google Scholar
[4]	L. H. Lim, Singular values and eigenvalues of tensors: a variational approach,, in, 1 (2005), 129. Google Scholar
[5]	M. Ng, L. Qi and G. Zhou, Finding the largest eigenvalue of a non-negative tensor,, SIAM J. Matrix Anal. Appl., 31 (2009), 1090. doi: 10.1137/09074838X. Google Scholar
[6]	L. Qi, Eigenvalues of a real supersymmetric tensor,, J. Symbolic Comput., 40 (2005), 1302. doi: 10.1016/j.jsc.2005.05.007. Google Scholar
[7]	L. Qi, F. Wang and Y. Wang, Z-eigenvalue methods for a global polynomial optimization problem,, Math. Program., 118 (2009), 301. doi: 10.1007/s10107-007-0193-6. Google Scholar
[8]	L. Qi, G. Yu and E. X. Wu, Higher order positive semi-definite diffusion tensor imaging,, SIAM J. Imaging Sci., 3 (2010), 416. Google Scholar
[9]	Y. Yang and Q. Z. Yang, Further results for Perron-Frobenius theorem for nonnegative tensors,, SIAM J. Matrix Anal. Appl., 31 (2010), 2517. doi: 10.1137/090778766. Google Scholar

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