A Nontrivial Solution To a Stochastic Matrix Equation
Document Type
Article
Publication Date
5-28-2015
Department
Mathematics
School
Mathematics and Natural Sciences
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.
Publication Title
East Asian Journal on Applied Mathematics
Volume
2
Issue
4
First Page
277
Last Page
284
Recommended Citation
Ding, J.,
Rhee, N.
(2015). A Nontrivial Solution To a Stochastic Matrix Equation. East Asian Journal on Applied Mathematics, 2(4), 277-284.
Available at: https://aquila.usm.edu/fac_pubs/20969