Volume 2, Issue 4
A Nontrivial Solution to a Stochastic Matrix Equation

J. Ding & N. H. Rhee

East Asian J. Appl. Math.,2 (2012), pp. 277-284.

Published online: 2018-02

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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 equation Brouwer's fixed point theorem

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@Article{EAJAM-2-277, author = {J. Ding and N. H. Rhee}, title = {A Nontrivial Solution to a Stochastic Matrix Equation}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {2}, number = {4}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.150512.231012a}, url = {http://global-sci.org/intro/article_detail/eajam/10877.html} }
TY - JOUR T1 - A Nontrivial Solution to a Stochastic Matrix Equation AU - J. Ding & N. H. Rhee JO - East Asian Journal on Applied Mathematics VL - 4 SP - 277 EP - 284 PY - 2018 DA - 2018/02 SN - 2 DO - http://doi.org/10.4208/eajam.150512.231012a UR - https://global-sci.org/intro/article_detail/eajam/10877.html KW - Matrix equation KW - Brouwer's fixed point theorem AB -

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.

J. Ding & N. H. Rhee. (1970). A Nontrivial Solution to a Stochastic Matrix Equation. East Asian Journal on Applied Mathematics. 2 (4). 277-284. doi:10.4208/eajam.150512.231012a
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