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

Abstract

We defifine the T-MPWG inverse of third-order F-square tensors by usingthe T-core EP decomposition of tensors via the T-product. Then, we presentsome characterizations and properties of the T-MPWG inverse. Moreover, theCayley-Hamilton theorem of the third-order tensors is extended to T-MPWGinverses. Examples are also given to illustrate these results.