  The notion of the Drazin inverse of an even-order tensor 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 producing a few characterizations of the Drazin inverse and the
W-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 to the
multilinear systems using the Drazin inverse and iterative (higher order
Gauss-Seidel) method of tensors. Besides this, the convergence analysis of the
iterative technique is also investigated within the framework of the Einstein
product.
