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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

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.
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
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##### References:
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