The MPWG inverse of third-order F-square tensors based on the T-product

We define the T-MPWG inverse of third-order F-square tensors by using the T-core EP decomposition of tensors via the T-product. Then, we present some characterizations and properties of the T-MPWG inverse. Moreover, the Cayley-Hamilton theorem of the third-order tensors is extended to T-MPWG inverses. Examples are also given to illustrate these results.