stochastic matrix


Let I be a finite or countable set, and let 𝐏=(pij:i,jI) be a matrix and let all pij be nonnegative. We say 𝐏 is stochastic if


for every jI. We call 𝐏 doubly stochastic if, in addition,


for all iI. Equivalently, 𝐏 is stochastic if every column is a distributionPlanetmathPlanetmath, and doubly stochastic if, in addition, every row is a distribution.

Stochastic and doubly stochastic matrices are common in discussions of random processes, particularly Markov chainsMathworldPlanetmath.

Title stochastic matrix
Canonical name StochasticMatrix
Date of creation 2013-03-22 12:37:29
Last modified on 2013-03-22 12:37:29
Owner mathwizard (128)
Last modified by mathwizard (128)
Numerical id 9
Author mathwizard (128)
Entry type Definition
Classification msc 60G99
Classification msc 15A51
Related topic Distribution
Related topic Matrix
Defines doubly stochastic
Defines stochastic matrix