Nondegeneracy of eigenvectors and singular vector tuples of tensors

04/13/2021

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by   Shenglong Hu, et al.

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In this article, nondegeneracy of singular vector tuples, Z-eigenvectors and eigenvectors of tensors is studied. They have found many applications in diverse areas. The main results are: (i) each (Z-)eigenvector/singular vector tuple of a generic tensor is nondegenerate, and (ii) each nonzero Z-eigenvector/singular vector tuple of an orthogonally decomposable tensor is nondegenerate.