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A Nontrivial Solution to a Stochastic Matrix Equation

A Nontrivial Solution to a Stochastic Matrix Equation
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Year:    2012

East Asian Journal on Applied Mathematics, Vol. 2 (2012), Iss. 4 : pp. 277–284

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.150512.231012a

East Asian Journal on Applied Mathematics, Vol. 2 (2012), Iss. 4 : pp. 277–284

Published online:    2012-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    8

Keywords:    Matrix equation Brouwer's fixed point theorem.

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