Moore-Penrose inverse of tensors via Einstein product

• 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

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...