𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Additive results for the Drazin inverse of block matrices and applications

✍ Scribed by Jelena Ljubisavljević; Dragana S. Cvetković-Ilić

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
222 KB
Volume
235
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, we consider the Drazin inverse of a sum of two matrices and derive additive formulas under conditions weaker than those used in some recent papers on the subject. As a corollary we get the main results from the paper of Yang and Liu [H. Yang, X. Liu, The Drazin inverse of the sum of two matrices and its applications, J. Comput. Appl. Math. 235 (2011Math. 235 ( ) 1412Math. 235 ( -1417]]. As an application we give some new representations for the Drazin inverse of a block matrix.

📜 SIMILAR VOLUMES

Additive results for the Wg–Drazin inver
Additive results for the Wg–Drazin inverse
✍ Dijana Mosić; Dragan S. Djordjević 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 182 KB

In this paper we prove the formula for the expression (A + B) d,W in terms of A, B, W , A d,W , B d,W , assuming some conditions for A, B and W . Here S d,W denotes the generalized W -weighted Drazin inverse of a linear bounded operator S on a Banach space.

A note on the representations for the Dr
A note on the representations for the Drazin inverse of 2 × 2 block matrices
✍ Xiezhang Li; Yimin Wei 📂 Article 📅 2007 🏛 Elsevier Science 🌐 English ⚖ 126 KB

In 1979, Campbell and Meyer proposed the problem of finding a formula for the Drazin inverse of a 2 × 2 matrix M = A B C D in terms of its various blocks, where the blocks A and D are required to be square matrices. Special cases of the problems have been studied. In particular, a representation of