Moore–Penrose inverse of tensors via Einstein product. Issue 4 (2nd April 2016)

• Record Type: Journal Article
• Authors: Sun, Lizhu; Zheng, Baodong; Bu, Changjiang; Wei, Yimin
• Is Part Of: Linear & multilinear algebra. Volume 64:Issue 4(2016)
• Page Start: 686
• Page End: 698
• Publication Date: 2016-04-02
• Subjects: tensor -- Moore–Penrose inverse -- multilinear system; 15A69 -- 15A09; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2015.1083933
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : 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.