Abstract:

Tensor generalized inverse is one of the important contents of tensor theory research. In this paper, based on the research of tensor generalized inverse in recent years, we obtain some properties of the core inverse of tensor with the Einstein product, a tensor partial ordering based on the core inverse and the least-squares solution of $ {{\cal A}} {*}{{\cal X}}={{\cal B}}$ under condition ${{\cal X}}\in{\Bbb {\cal R}}({{\cal A}}) $.

Key words: Core inverse, Einstein product, Partial ordering, Tensor equation