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Mathematics-Online lexicon: Annotation to

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 $ x_i$ according to

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

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  automatisch erstellt am 19.  8. 2013