An extension of the Moore-Penrose Inverse of a Tensor via the Einstein product

Abstract

In this paper, we first give an expression for the Moore-Penrose inverse of the product of two tensors via the Einstein product. We then introduce a new generalized inverse of a tensor called product Moore-Penrose inverse. A necessary and sufficient condition for the coincidence of the Moore-Penrose inverse and the product Moore-Penrose inverse is also proposed. Finally, the triple reverse order law of tensors is introduced.

References in corpus (3)

• On degeneration of tensors and algebras
• Further results on generalized inverses of tensors via the Einstein product
• Reverse order law for the Moore-Penrose inverses of tensors

Cited by in corpus (5)

• Weighted Moore-Penrose inverses of arbitrary-order tensors
• Reverse-order law for weighted Moore--Penrose inverse of tensors
• A note on numerical ranges of tensors
• On reverse-order law of tensors and its application to additive results on Moore-Penrose inverse
• Numerical range for weighted Moore-Penrose inverse of tensor