Basics of Tensor Rank

Part of the SpringerBriefs in Statistics book series (BRIEFSSTATIST)


In statistical data analysis, a tensor is a multi-array datum. Just as the complexity of a matrix datum is described by its matrix rank, the complexity of a tensor datum is described by its tensor rank. In this chapter, we review several concepts of tensor rank such as rank-1 tensors and tensor flattening.


Kronecker Product Maximal Rank Nonzero Vector Matrix Rank Tensor Rank 

Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Toshio Sakata
    • 1
  • Toshio Sumi
    • 2
  • Mitsuhiro Miyazaki
    • 3
  1. 1.Faculty of DesignKyushu UniversityFukuokaJapan
  2. 2.Faculty of Arts and ScienceKyushu UniversityFukuokaJapan
  3. 3.Department of MathematicsKyoto University of EducationKyotoJapan

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