Frontiers of Mathematics in China >
lk,s-Singular values and spectral radius of rectangular tensors
Received date: 28 Apr 2012
Accepted date: 12 Nov 2012
Published date: 01 Feb 2013
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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.
Chen LING , Liqun QI . lk,s-Singular values and spectral radius of rectangular tensors[J]. Frontiers of Mathematics in China, 2013 , 8(1) : 63 -83 . DOI: 10.1007/s11464-012-0265-7
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