## Abstract and Applied Analysis

### A Generalization of the SMW Formula of Operator $A+YG{Z}^{*}$ to the $\left\{2\right\}$-Inverse Case

Yingtao Duan

#### Abstract

The classical Sherman-Morrison-Woodbury (for short SMW) formula ${\left(A+YG{Z}^{*}\right)}^{-1}={A}^{-1}-{A}^{-1}Y{\left({G}^{-1}+{Z}^{*}{A}^{-1}Y\right)}^{-1}{Z}^{*}{A}^{-1}$ is generalized to the $\left\{2\right\}$-inverse case. Some sufficient conditions under which the SMW formula can be represented as ${\left(A+YG{Z}^{*}\right)}^{-}={A}^{-}-{A}^{-}Y{\left({G}^{-}+{Z}^{*}{A}^{-}Y\right)}^{-}{Z}^{*}{A}^{-}$ are obtained.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 694940, 4 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393512070

Digital Object Identifier
doi:10.1155/2013/694940

Mathematical Reviews number (MathSciNet)
MR3108663

#### Citation

Duan, Yingtao. A Generalization of the SMW Formula of Operator $A+YG{Z}^{*}$ to the $\left\{2\right\}$ -Inverse Case. Abstr. Appl. Anal. 2013 (2013), Article ID 694940, 4 pages. doi:10.1155/2013/694940. https://projecteuclid.org/euclid.aaa/1393512070

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