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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Bibliographic Details
Published in:	Linear & multilinear algebra Vol. 64; no. 4; pp. 686 - 698
Main Authors:	Sun, Lizhu, Zheng, Baodong, Bu, Changjiang, Wei, Yimin
Format:	Journal Article
Language:	English
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
Online Access:	Get full text
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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.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23
ISSN:	0308-1087 1563-5139
DOI:	10.1080/03081087.2015.1083933