A NOTE ON THE STOCHASTIC ROOTS OF STOCHASTIC MATRICES

In this paper, we study the stochastic root matrices of stochastic matrices. All stochastic roots of2×2 stochastic matrices are found explicitly.A method based on characteristic polynomial of matrix isdeveloped to find all real root matrices that are functions of the original 3×3 matrix, including allpossible(function)stochastic root matrices. In addition, we comment on some numerical methods forcomputing stochastic root matrices of stochastic matrices.

A note on the stochastic roots of stochastic matrices

In this paper, we study the stochastic root matrices of stochastic matrices. All stochastic roots of 2×2 stochastic matrices are found explicitly. A method based on characteristic polynomial of matrix is developed to find all real root matrices that are functions of the original 3×3 matrix, including all possible (function) stochastic root matrices. In addition, we comment on some numerical methods for computing stochastic root matrices of stochastic matrices. Qi-Ming He is currently an associate professor in the Industrial Engineering Department at Dalhousie University. He received a Ph.D from the Institute of Applied Mathematics, Chinese Academy of Sciences in 1989 and a Ph.D from the Department of Management Science at the University of Waterloo in 1996. His main research areas are algorithmic methods in applied probability, queuing theory, inventory control, and production management. In investigating various stochastic models, his favourite methods are matrix analytic methods. Recently, he is working on queuing systems with multiple types of customers and inventory systems with multiple types of demands. Eldon Gunn is currently a professor in the Industrial Engineering Department at Dalhousie University. He received a Ph.D from the University of Toronto in 1981. His research involves the application of operations research methods to production planning, particularly in the natural resource sector. His other research interest includes stochastic programming, routing and scheduling, control of queuing processes and inventory control.