Stochastic Matrix

A stochastic matrix is a Square Matrix whose columns are Probability Vectors.

|det(P)| ⇐ 1, only volume contracting or preserving

Theorem as

If is a regular stochastic matrix, then has a unique steady-state vector , and converges to as ; where

Regular

• Stochastic matrix is regular if there strictly has positive entries
• Regular unique steady state vectors
• Irregular steady state vectors