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