A study on the 1- inverse of tensors via the M-Product
Abstract
In this paper, we will study the issue about the 1- inverse, where ∈\, D, *\, via the M-product. The aim of the current study is threefold. Firstly, the definition and characteristic of the 1- inverse is introduced. Equivalent conditions for a tensor to be a 1- inverse are established. Secondly, using the singular value decomposition, the corresponding numerical algorithms for computing the 1- inverse are given. Finally, the solutions of the multilinear equations related 1- inverse are studied, and numerical calculations are given to verify our conclusions.
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