Everything about Stochastic Matrix totally explained
In
mathematics, a
stochastic matrix,
probability matrix, or
transition matrix is used to describe the transitions of a
Markov chain. It has found use in
probability theory,
statistics and
linear algebra, as well as
computer science. There are several different definitions and types of stochastic matrices;
» A
right stochastic matrix is a square
matrix each of whose rows consists of nonnegative
real numbers, with each row summing to 1.
» A
left stochastic matrix is a square matrix whose columns consist of nonnegative real numbers whose sum is 1.
» A
doubly stochastic matrix where all entries are nonnegative and all rows and all columns sum to 1.
A common
convention in
English language mathematics literature is to use the right stochastic matrix; this convention will be used in this article.
In the same vein, one may define a
stochastic vector as a
vector whose elements consist of nonnegative real numbers which sum to 1. Thus, each row (or column) of a stochastic matrix is a stochastic vector. Stochastic vectors are also sometimes called
probability vectors.
Definition and properties
A stochastic matrix describes a Markov chain
.
Further Information
Get more info on 'Stochastic Matrix'.
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