Generalized bilateral inverses of tensors via Einstein product with applications to singular tensor equations

In this paper, a unified approach for various extended inverses of tensors, the generalized bilateral inverse of tensors via Einstein products, is introduced and we show that a number of known generalized tensor inverses can be regarded as special cases of this idea. Some characterizations of the CMP, DMP, and MPD inverse of tensors by using Einstein products are provided. The notion of generalized bilateral inverses' dual and self-duality are investigated. In addition, the bilateral inverse solutions for singular linear tensor equations are studied.