Further results on the Drazin inverse of even‐order tensors

Abstract

SummaryThe notion of the Drazin inverse of an even‐order tensors with the Einstein product was introduced, very recently [J. Ji and Y. Wei. Comput. Math. Appl., 75(9), (2018), pp. 3402‐3413]. In this article, we further elaborate this theory by establishing a few characterizations of the Drazin inverse and ‐weighted Drazin inverse of tensors. In addition to these, we compute the Drazin inverse of tensors using different types of generalized inverses and full rank decomposition of tensors. We also address the solution of multilinear systems by using the Drazin inverse and iterative (higher order Gauss‐Seidel) method of tensors. Besides these, the convergence analysis of the iterative technique is also investigated within the framework of the Einstein product.