About the maximal rank of 3-tensors over the real and the complex number field

作者：Sumi Toshio^*; Miyazaki Mitsuhiro; Sakata Toshio

来源：Annals of the Institute of Statistical Mathematics, 2010, 62(4): 807-822.

DOI：10.1007/s10463-010-0294-5

• Tensor
• Maximal rank

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.

• 出版日期2010-8