About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 216035, 4 pages
http://dx.doi.org/10.1155/2013/216035
Research Article

Existence and Uniqueness of the Positive Definite Solution for the Matrix Equation

Department of Mathematics, Heze University, Heze, Shandong 274015, China

Received 15 May 2013; Revised 23 June 2013; Accepted 4 July 2013

Academic Editor: Vejdi I. Hasanov

Copyright © 2013 Dongjie Gao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the nonlinear matrix equation , where is positive definite, is positive semidefinite, and is the block diagonal matrix defined by . We prove that the equation has a unique positive definite solution via variable replacement and fixed point theorem. The basic fixed point iteration for the equation is given.