The generalized inverses of tensors and an application to linear models

被引：52
|
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
收藏
页码：385 / 397
页数：13
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