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 - <p style="text-align: justify;">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.</p>