Generalized inverses of tensors via a general product of tensors

doi:10.1007/s11464-018-0695-y

Front. Math. China

2018, Vol. 13

Issue (4) : 893-911 https://doi.org/10.1007/s11464-018-0695-y

RESEARCH ARTICLE

Generalized inverses of tensors via a general product of tensors

Lizhu SUN¹, Baodong ZHENG², Yimin WEI³, Changjiang BU¹(

)

¹. College of Science, Harbin Engineering University, Harbin 150001, China
². School of Science, Harbin Institute of Technology, Harbin 150001, China
³. School of Mathematical Sciences, Shanghai Key Laboratory of Contemporary Applied Mathematics, Fudan University, Shanghai 200433, China

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Abstract

We define the {i}-inverse (i = 1; 2; 5) and group inverse of tensors based on a general product of tensors. We explore properties of the generalized inverses of tensors on solving tensor equations and computing formulas of block tensors. We use the {1}-inverse of tensors to give the solutions of a multilinear system represented by tensors. The representations for the {1}-inverse and group inverse of some block tensors are established.

Keywords Tensor generalized inverse tensor equation general product of tensor

Corresponding Author(s): Changjiang BU

Issue Date: 14 August 2018

Cite this article:

Lizhu SUN,Baodong ZHENG,Yimin WEI, et al. Generalized inverses of tensors via a general product of tensors[J]. Front. Math. China, 2018, 13(4): 893-911.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-018-0695-y
https://academic.hep.com.cn/fmc/EN/Y2018/V13/I4/893

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