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

摘要

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: , if p is even, if or n is odd, and if m < n where stands for or .