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A Nontrivial Solution to a Stochastic Matrix Equation

Published online by Cambridge University Press:  28 May 2015

J. Ding  and
N. H. Rhee
J. Ding*
Affiliation:
Department of Mathematics, The University of Southern Mississippi, Hattiesburg, MS 39406-5045, USA
N. H. Rhee*
Affiliation:
Department of Mathematics and Statistics, University of Missouri - Kansas City, Kansas City, MO 64110-2499, USA
*
Corresponding author. Email: [email protected]
Corresponding author. Email: [email protected]
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Abstract.

If A is a nonsingular matrix such that its inverse is a stochastic matrix, the classic Brouwer fixed point theorem implies that the matrix equation AXA = XAX has a nontrivial solution. An explicit expression of this nontrivial solution is found via the mean ergodic theorem, and fixed point iteration is considered to find a nontrivial solution.

Keywords

Matrix equationBrouwer's fixed point theorem
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 2 , Issue 4 , November 2012 , pp. 277 - 284
Copyright
Copyright © Global-Science Press 2012

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