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Nondegeneracy of eigenvectors and singular vector tuples of tensors

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Abstract

In this article, nondegeneracy of singular vector tuples, Z-eigenvectors and eigenvectors of tensors is studied, which 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.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 11771328), Young Elite Scientists Sponsorship Program by Tianjin and the Natural Science Foundation of Zhejiang Province of China (Grant No. LD19A010002). The author is grateful to Professor Donghui Li at South China Normal University for valuable suggestions.

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

    Shenglong Hu

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  1. Shenglong Hu
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Correspondence to Shenglong Hu.

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Hu, S. Nondegeneracy of eigenvectors and singular vector tuples of tensors. Sci. China Math. 65, 2483–2492 (2022). https://doi.org/10.1007/s11425-020-1863-5

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  • DOI: https://doi.org/10.1007/s11425-020-1863-5

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