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l k,s-Singular values and spectral radius of rectangular tensors

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Abstract

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 l k,s-singular values/vectors of real partially symmetric rectangular tensors. Then, based upon the presented properties of l k,s-singular values /vectors, some properties of the related l k,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.

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Authors and Affiliations

  1. School of Science, Hangzhou Dianzi University, Hangzhou, 310018, China

    Chen Ling

  2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China

    Liqun Qi

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  1. Chen Ling
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  2. Liqun Qi
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Correspondence to Chen Ling.

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Ling, C., Qi, L. l k,s-Singular values and spectral radius of rectangular tensors. Front. Math. China 8, 63–83 (2013). https://doi.org/10.1007/s11464-012-0265-7

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  • DOI: https://doi.org/10.1007/s11464-012-0265-7

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