Frontiers of Mathematics in China >
Jordan canonical form of three-way tensor with multilinear rank (4,4,3)
Received date: 09 Sep 2018
Accepted date: 11 Jan 2019
Published date: 15 Apr 2019
Copyright
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 with multilinear rank (4,4,3), we show that must be turned into the canonical form if the upper triangular entries of the last three slices of are nonzero. If some of the upper triangular entries of the last three slices of are zeros, we give some conditions to guarantee that can be turned into the canonical form.
Key words: Jordan canonical form; tensor decomposition; multilinear rank
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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