The generalized inverses of tensors and an application to linear models

被引：53

作者：

Jin, Hongwei ^{[1
,2
]}

Bai, Minru ^{[1
]}

Benitez, Julio ^{[2
]}

Liu, Xiaoji ^{[3
]}

机构：

[1] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China

[2] Univ Politecn Valencia, Dept Matemat Aplicada, Inst Matemat Multidisciplinar, Camino Vera S-N, Valencia 46022, Spain

[3] Guangxi Univ Nationalities, Fac Sci, Nanning 530006, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2017年 / 74卷 / 03期

基金：

美国国家科学基金会;

关键词：

Tensors; Generalized inverses; Moore-Penrose inverse of tensors; Linear models;

D O I：

10.1016/j.camwa.2017.04.017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we recall and extend some tensor operations. Then, the generalized inverse of tensors is established by using tensor equations. Moreover, we investigate the least-squares solutions of tensor equations. An algorithm to compute the Moore-Penrose inverse of an arbitrary tensor is constructed. Finally, we apply the obtained results to higher order Gauss-Markov theorem. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：385 / 397

页数：13

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