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Frontiers of Mathematics in China

, Volume 14, Issue 2, pp 281–300 | Cite as

Jordan canonical form of three-way tensor with multilinear rank (4,4,3)

  • Lubin Cui
  • Minghui LiEmail author
Research Article
  • 8 Downloads

Abstract

The Jordan canonical form of matrix is an important concept in linear algebra. And the concept has been extended to three-way arrays case. In this paper, we study the Jordan canonical form of three-way tensor with multilinear rank (4,4,3). For a 4×4×4 tensor Gj with multilinear rank (4,4,3), we show that Gj must be turned into the canonical form if the upper triangular entries of the last three slices of Gj are nonzero. If some of the upper triangular entries of the last three slices of Gj are zeros, we give some conditions to guarantee that Gj can be turned into the canonical form.

Keywords

Jordan canonical form tensor decomposition multilinear rank 

MSC

15A18 15A69 

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Notes

Acknowledgements

This work was supported in part by the National Natural Science Foundations of China (Grant Nos. 11601134, 11526083, 11571905, 11601133) and Guangdong Provincial Engineering Technology Research Center for Data Science (No. 2016KF01).

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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal ControlSchool of Mathematics and Information Sciences, Henan Normal UniversityXinxiangChina

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