Reverse order law for the Moore-Penrose inverses of tensors

TL;DR

This paper investigates the reverse order law for Moore-Penrose inverses of tensors, providing new identities and conditions under which the law holds, advancing theoretical understanding in multilinear algebra.

Contribution

It introduces new identities and necessary conditions for the reverse order law of Moore-Penrose tensor inverses using Einstein product, expanding existing theoretical frameworks.

Findings

Derived new identities involving Moore-Penrose inverses of tensors.

Established necessary and sufficient conditions for the reverse order law.

Enhanced theoretical understanding of tensor inverse properties.

Abstract

Reverse order law for the Moore-Penrose inverses of tensors are useful in the field of multilinear algebra. In this paper, we first prove some more identities involving the Moore-Penrose inverse of tensors. We then obtain a few necessary and sufficient conditions for the reverse order law for the Moore-Penrose inverse of tensors via the Einstein product.