The 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 $𝒲$‐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 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.

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关于偶数张量Drazin逆的进一步结果

爱因斯坦积的偶数阶张量的Drazin逆的概念是最近才提出的[J．纪和魏 计算 数学。Appl。，75（9），（2018），第3402–3413页]。在本文中，我们将通过建立Drazin逆和$𝒲$张量的加权Drazin逆。除了这些，我们还使用不同类型的广义逆和张量的全秩分解来计算张量的Drazin逆。我们还使用张量的Drazin逆和迭代（高阶高斯-赛德尔）方法来解决多线性系统的解决方案。除此之外，还在爱因斯坦积的框架内研究了迭代技术的收敛性分析。