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A note on the solvability of a tensor equation

This work is partially supported by National Science Foundation of China (Grant No. 11771328), Young Elite Scientists Sponsorship Program by Tianjin, and the Natural Science Foundation of Zhejiang Province, China (Grant No. LD19A010002)

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  • In this note, we generalize a solvability result for a tensor equation with a nonsingular leading tensor to the case with possibly a singular leading tensor.

    Mathematics Subject Classification: Primary: 15A18; Secondary: 15A69.

    Citation:

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  • [1] S. Friedland, Inverse eigenvalue problem, Linear Algebra Appl., 17 (1977), 15-51.  doi: 10.1016/0024-3795(77)90039-8.
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    [3] S. HuZ.-H. HuangC. Ling and L. Qi, On determinants and eigenvalue theory of tensors, J. Symb. Comput., 50 (2013), 508-531.  doi: 10.1016/j.jsc.2012.10.001.
    [4] Z.-H. Huang and L. Qi, Tensor complementarity problems–Part I: Basic theory, J. Optim. Theory Appl., 183 (2019), 1-23.  doi: 10.1007/s10957-019-01566-z.
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    [6] X. WangM. Che and Y. Wei, Existence and uniqueness of positive solution for $H^+$-tensor equations, Appl. Math. Lett., 98 (2019), 191-198.  doi: 10.1016/j.aml.2019.05.046.
    [7] X. Wang, M. Che and Y. Wei, Neural network approach for solving nonsingular multi-linear tensor systems, J. Comput. Appl. Math., 368 (2020), 112569. doi: 10.1016/j.cam.2019.112569.
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