Mathematics-Online lexicon: Stochastic Matrices

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	Mathematics-Online lexicon:
	Stochastic Matrices

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A given matrix $P\in\mathbb{R}^{n\times n}$ is called stochastic if $p_{i,j}\ge 0$ and

$\displaystyle \sum_{j=1}^n p_{i,j} = 1,\quad i=1,\ldots,n\, .$

Stochastic matrices describe the change of probabilities

according to

$\displaystyle x'_j = \sum_i x_i p_{i,j}\, .$

(Authors: App/Burkhardt/Höllig)

see also:

automatically generated 7/ 8/2004