stochastic matrix
Definition
Let be a finite or countable set, and let be a matrix and let all be nonnegative. We say is stochastic if
for every . We call doubly stochastic if, in addition,
for all . Equivalently, is stochastic if every column is a distribution, 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 chains.
Title | stochastic matrix |
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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 |