Tensor data are becoming important recently in various application fields. In this paper, we consider themaximal 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.rankR(m, n, p) ≤ m + [p/2]n, max.rankR(n, n, p) ≤ (p+1)n/2 if p is even, max.rankF(n, n, 3) ≤ 2n-1 if F = C or n is odd, and max.rankF(m, n, 3) ≤ m +n-1 if m < n where F stands for ℝ or ℂ .
|Number of pages||16|
|Journal||Annals of the Institute of Statistical Mathematics|
|Publication status||Published - Aug 2010|
All Science Journal Classification (ASJC) codes
- Statistics and Probability