## Stochastic Matrix

A Stochastic matrix is the transition matrix for a finite Markov Chain, also called a Markov Matrix. Elements of the matrix must be Real Numbers in the Closed Interval [0, 1].

A completely independent type of stochastic matrix is defined as a Square Matrix with entries in a Field such that the sum of elements in each column equals 1. There are two nonsingular Stochastic Matrices over (i.e., the integers mod 2),

There are six nonsingular stochastic Matrices over ,

In fact, the set of all nonsingular stochastic matrices over a Field forms a Group under Matrix Multiplication. This Group is called the Stochastic Group.

Poole, D. G. The Stochastic Group.'' Amer. Math. Monthly 102, 798-801, 1995.