Tensor data are becoming important recently in various application fields. In this paper, we consider the maximal rank problem of 3-tensors and extend Atkinson and Stephens' and Atkinson and Lloyd's results over the real number field. We also prove the assertion of Atkinson and Stephens: max.rank(R)(m, n, p) <= m + [p/2]n, max.rank(R)(n, n, p) <= (p+ 1)n/2 if p is even, max.rank(F)(n, n, 3) <= 2n-1 if F = C or n is odd, and max.rank(F)(m, n, 3) <= m + n-1 if m < n where F stands for R or C.
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机译：张量数据最近在各个应用领域中变得越来越重要。在本文中，我们考虑了三张量的最大秩问题，并将Atkinson和Stephens以及Atkinson和Lloyd的结果扩展到实数域。我们还证明了Atkinson和Stephens的主张：max.rank（R）（m，n，p）<= m + [p / 2] n，max.rank（R）（n，n，p）<=（ p + 1）n / 2（如果p为偶数），则最大rank（F）（n，n，3）<= 2n-1，如果F = C或n为奇数，则最大rank（F）（m，n， 3）如果m 展开▼
