Minimum (maximum) rank of tensors and the sign nonsingular tensors

2014/12/23 by Bu, Changjiang, Wang, Wenzhe, Sun, Lizhu +1
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1412.7413

Abstract

In this paper, we define the minimum (maximum) rank, term rank and the sign nonsingular of tensors. The sufficiency and necessity for the minimum rank of a real tensor to be 1 is given. And we show that the maximum rank of a tensor is not less than the term rank. We also prove that the minimum rank of a sign nonsingular tensor is not less than the dimension of it. And we get some characterizations of a tensor having sign left or sign right inverses.

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