On Comon’s conjecture over arbitrary fields
On Comon’s conjecture over arbitrary fields
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关于任意域上的科蒙猜想
DOI：
10.1016/j.laa.2019.11.010
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
JinliXu
中科院分区：
文献类型：
--
作者：
Baodong Zheng;RiguangHuang;XiaoyuSong;JinliXu
Comon's Conjecture asserts that for a symmetric tensor, the rank is equal to the symmetric rank. For the field of real numbers R or the field of complex numbers C, Zhang et al. proved the conjecture for the case that the rank of a symmetric tensor does not exceed the order. In this paper, we show that over arbitrary fields this conjecture is true when the rank of a tensor is less than its order. Moreover, we construct a counterexample in which the rank of a symmetric tensor whose rank equals its order.
