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

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.

Keywords

Nonnegative rectangular tensor / lk / ^s-singular value / lk / ^s-spectral radius / irreducibility / weak irreducibility

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