RESEARCH ARTICLE

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

  • Lubin Cui ,
  • Minghui Li
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  • Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, School of Mathematics and Information Sciences, Henan Normal University, Xinxiang 453007, China

Received date: 09 Sep 2018

Accepted date: 11 Jan 2019

Published date: 15 Apr 2019

Copyright

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

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.

Cite this article

Lubin Cui , Minghui Li . Jordan canonical form of three-way tensor with multilinear rank (4,4,3)[J]. Frontiers of Mathematics in China, 2019 , 14(2) : 281 -300 . DOI: 10.1007/s11464-019-0747-y

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