TY - JOUR T1 - A Nontrivial Solution to a Stochastic Matrix Equation 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, 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.