Moore-Penrose inverse of tensors via Einstein product

In this paper, we define the Moore-Penrose inverse of tensors with the Einstein product, and the explicit formulas of the Moore-Penrose inverse of some block tensors are obtained. The general solutions of some multilinear systems are given and we also give the minimum-norm least-square solution of s...

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Published inLinear & multilinear algebra Vol. 64; no. 4; pp. 686 - 698
Main Authors Sun, Lizhu, Zheng, Baodong, Bu, Changjiang, Wei, Yimin
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.04.2016
Taylor & Francis Ltd
Subjects
Algebra
Blocking
Inverse
Least squares method
Mathematical analysis
Moore-Penrose inverse
multilinear system
tensor
Tensors
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Summary:In this paper, we define the Moore-Penrose inverse of tensors with the Einstein product, and the explicit formulas of the Moore-Penrose inverse of some block tensors are obtained. The general solutions of some multilinear systems are given and we also give the minimum-norm least-square solution of some multilinear systems using the Moore-Penrose inverse of tensors.
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ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2015.1083933