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Volume 12, Issue 3
A Semi-Tensor Product of Tensors and Applications

Wei-Hui Liu, Ze-Jia Xie & Xiao-Qing Jin

DOI: 10.4208/eajam.181120.050122

East Asian J. Appl. Math., 12 (2022), pp. 696-714.

Published online: 2022-04

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  • Abstract

A semi-tensor product of matrices is proposed as a generalization of usual matrix product in the case where the dimensions of two factor matrices do not match. The properties of the semi-tensor product of tensors and swap tensors based on the Einstein product are studied. Applications of this new tensor product in image restoration and in finite dimensional algebras are discussed.

  • Keywords

Semi-tensor product, tensor, Einstein product, Kronecker product, swap tensor.

  • AMS Subject Headings

15A52, 15A45, 60F25, 65H35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-12-696, author = {Wei-Hui Liu, Ze-Jia Xie and Xiao-Qing Jin}, title = {A Semi-Tensor Product of Tensors and Applications}, journal = {East Asian Journal on Applied Mathematics}, year = {2022}, volume = {12}, number = {3}, pages = {696--714}, abstract = {

A semi-tensor product of matrices is proposed as a generalization of usual matrix product in the case where the dimensions of two factor matrices do not match. The properties of the semi-tensor product of tensors and swap tensors based on the Einstein product are studied. Applications of this new tensor product in image restoration and in finite dimensional algebras are discussed.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.181120.050122}, url = {http://global-sci.org/intro/article_detail/eajam/20414.html} }
TY - JOUR T1 - A Semi-Tensor Product of Tensors and Applications AU - Wei-Hui Liu, Ze-Jia Xie & Xiao-Qing Jin JO - East Asian Journal on Applied Mathematics VL - 3 SP - 696 EP - 714 PY - 2022 DA - 2022/04 SN - 12 DO - http://doi.org/10.4208/eajam.181120.050122 UR - https://global-sci.org/intro/article_detail/eajam/20414.html KW - Semi-tensor product, tensor, Einstein product, Kronecker product, swap tensor. AB -

A semi-tensor product of matrices is proposed as a generalization of usual matrix product in the case where the dimensions of two factor matrices do not match. The properties of the semi-tensor product of tensors and swap tensors based on the Einstein product are studied. Applications of this new tensor product in image restoration and in finite dimensional algebras are discussed.

Wei-Hui Liu, Ze-Jia Xie and Xiao-Qing Jin. (2022). A Semi-Tensor Product of Tensors and Applications. East Asian Journal on Applied Mathematics. 12 (3). 696-714. doi:10.4208/eajam.181120.050122
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