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The generalized inverses of tensors via the C-Product

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arxiv 2211.02841 v2 pith:PCKQLFW4 submitted 2022-11-05 math.RA

Hongwei Jin , Shumin Xu , Hongjie Jiang , Xiaoji Liu This is my paper · ORCID
classification math.RA
keywords inversetensorsc-productgeneralizedinversesalongdrazinmoore-penrose
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This paper studies the issues about the generalized inverses of tensors under the C-Product. The aim of this paper is threefold. Firstly, this paper present the definition of the Moore-Penrose inverse, Drazin inverse of tensors under the C-Product. Moreover, the inverse along a tensor is also introduced. Secondly, this paper gives some other expressions of the generalized inverses of tensors by using several decomposition forms of tensors. Finally, the algorithms for the Moore-Penrose inverse, Drazin inverse of tensors and the inverse along a tensor are established.

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