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

doi:10.1007/s11464-019-0747-y

Front. Math. China

2019, Vol. 14

Issue (2) : 281-300 https://doi.org/10.1007/s11464-019-0747-y

RESEARCH ARTICLE

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

Lubin Cui, Minghui Li(

)

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

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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 $G j$ with multilinear rank (4,4,3), we show that $G j$ must be turned into the canonical form if the upper triangular entries of the last three slices of $G j$ are nonzero. If some of the upper triangular entries of the last three slices of $G j$ are zeros, we give some conditions to guarantee that $G j$ can be turned into the canonical form.

Keywords Jordan canonical form tensor decomposition multilinear rank

Corresponding Author(s): Minghui Li

Issue Date: 14 May 2019

Cite this article:

Lubin Cui,Minghui Li. Jordan canonical form of three-way tensor with multilinear rank (4,4,3)[J]. Front. Math. China, 2019, 14(2): 281-300.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-019-0747-y
https://academic.hep.com.cn/fmc/EN/Y2019/V14/I2/281

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[1]	QI Liqun, SUN Wenyu, WANG Yiju. Numerical multilinear algebra and its applications[J]. Front. Math. China, 2007, 2(4): 501-526.

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