Moore–Penrose inverse of tensors via Einstein product

2015/09/04 by Lizhu Sun, Baodong Zheng, Changjiang Bu +1 · 8 citations
Mathematics · Computer Science · #Tensor decomposition and applications #Matrix Theory and Algorithms #Advanced Optimization Algorithms Research

paper · doi:10.1080/03081087.2015.1083933

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.

Cited by

• Further results on generalized inverses of tensors via the Einstein product
• A tensor phase theory with applications in multilinear control
• The k-core of a graph and its high-order spectra
• Moore-Penrose inverse of quaternion tensors via M-product with applications in color image classification
• Formulae for the Drazin inverse of modified tensors via the Einstein product
• Separability Criteria of Quantum States based on Generalized Bloch Representation
• The solvability conditions and exact solutions to some quaternion tensor systems
• T-Jordan Canonical Form and T-Drazin Inverse based on the T-Product

Related

• Further results on generalized inverses of tensors via the Einstein product
• An extension of the Moore-Penrose Inverse of a Tensor via the Einstein product
• Reverse order law for the Moore-Penrose inverses of tensors
• Reverse-order law for weighted Moore--Penrose inverse of tensors
• On reverse-order law of tensors and its application to additive results on Moore-Penrose inverse