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} }