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arXiv · 2211.02841

The generalized inverses of tensors via the C-Product

Hongwei Jin·Shumin Xu·Hongjie Jiang·Xiaoji Liu
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Abstract

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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Hongwei Jin, Shumin Xu, Hongjie Jiang, Xiaoji Liu. 2022-11-05. The generalized inverses of tensors via the C-Product. https://arxiv.org/abs/2211.02841

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