In this paper, let A and B be n x p complex tensors = + E. Denote the T-Drazin inverse of by AD. We give a perturbation bound for ||BD-AD||=||AD|| under condition (W). Considering solution singular tensor equation A* b, (b ? R(AD)) at same time. The optimal system equations have been given.

In this paper we offer new representations for Drazin inverse of block matrix, which recover some representations from current literature on this subject. 2000 Mathematics Subject Classification: 15A09

Let A be a complex unital Banach algebra with unit 1. The sets of all invertible and quasinilpotent elements (σ(a) = {0}) of A will be denoted by A and A, respectively. The group inverse of a ∈ A is the unique element a ∈ A which satisfies aaa = a, aaa = a, aa = aa. If the group inverse of a exists, a is group invertible. Denote by A the set of all group invertible elements of A. The generalize...

Several representations of the generalized Drazin inverse of a block matrix with a group invertible generalized Schur complement in Banach algebra are presented.

In this paper , some results about the index of matrix and Drazin inverse are given. We then explain applications of them in solving singular linear system of equations.

Given a bounded operator A on a Banach space X with Drazin inverse A and index r, we study the class of group invertible bounded operators B such that / + A (B — A) is invertible and 1Z(B) f]N(A) = {0}. We show that they can be written with respect to the decomposition X = lZ(A) 0 Af(A) as a matrix operator, B = ( _ _ __i _ ), where B\ and B\ + B\9#?1 a r e invertible. ^ if21 t>2\tf\ i*\2 Sever...