E-characteristic polynomials of real rectangular tensor |
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| Authors: | Wei Wu Xiaoxiao Chen |
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| Institution: | 1. School of Sciences, Tianjin University, Tianjin, 300072, China
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| Abstract: | By the resultant theory, the E-characteristic polynomial of a real rectangular tensor is defined. It is proved that an E-singular value of a real rectangular tensor is always a root of the E-characteristic polynomial. The definition of the regularity of square tensors is generalized to the rectangular tensors, and in the regular case, a root of the Echaracteristic polynomial of a special rectangular tensor is an E-singular value of the rectangular tensor. Moreover, the best rank-one approximation of a real partially symmetric rectangular tensor is investigated. |
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| Keywords: | E-characteristic polynomial rectangular tensor E-singular value rank-one approximation |
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