## TRANSITION PROBABILITY MATRIX
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A matrix which represents all the possible transitions from one state to any other in a Markovian system.

G. PASK describes it as follows: "P is an n.n matrix with n entries p_{ij} and Σp_{ij}= 1 rows and columns corresponding with the states J(t) in a column vector. Each row in the matrix represents the probability distribution obtained by selecting the state in correspondence with this row, as we do in multiplication with the column vector J(t). The state of a Markovian system can be represented as a point in a probability space with n co-ordinates p_{1}, p_{2}… p_{n} one to each state. This space should not be confused with the phase space with m co-ordinates related to the attributes" (1961a, p.122).

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### Publisher

Bertalanffy Center for the Study of Systems Science(2020).

To cite this page, please use the following information:

* Bertalanffy Center for the Study of Systems Science (2020).* Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]

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