lk,s-Singular values and spectral radius of rectangular tensors
lk,s-Singular values and spectral radius of rectangular tensors
Chen LING1(), Liqun QI2
1. School of Science, Hangzhou Dianzi University, Hangzhou 310018, China; 2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China
The real rectangular tensors arise from the strong ellipticity condition problem in solid mechanics and the entanglement problem in quantum physics. In this paper, we study the singular values/vectors problem of real nonnegative partially symmetric rectangular tensors. We first introduce the concepts of lk,s-singular values/vectors of real partially symmetric rectangular tensors. Then, based upon the presented properties of lk,s-singular values /vectors, some properties of the related lk,s-spectral radius are discussed. Furthermore, we prove two analogs of Perron-Frobenius theorem and weak Perron-Frobenius theorem for real nonnegative partially symmetric rectangular tensors.
. lk,s-Singular values and spectral radius of rectangular tensors[J]. Frontiers of Mathematics in China, 2013, 8(1): 63-83.
Chen LING, Liqun QI. lk,s-Singular values and spectral radius of rectangular tensors. Front Math Chin, 2013, 8(1): 63-83.
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