A Markov Chain is a stochastic model describing a sequence of possible events. Markov Chains have many different applications, such as predictive text, search engines (Google’s PageRank algorithm makes use of Markov Chains), cruise control in vehicles, and even currency exchange rates.

Markov Chains may be visualized as finite state automata, or as stochastic matrices with **transition vectors**. These vectors determine the odds of each event occuring, and will change after every transition. However this method of representing a Markov Chain will only work if the state space **finite**.

Although vectors are only a small part of Markov Chains as a whole, they still play a key role in helping us visualize them in a manageable way.

sources:

https://en.wikipedia.org/wiki/Markov_chain

http://www.sosmath.com/matrix/markov/markov.html

https://www.math.ucdavis.edu/~daddel/linear_algebra_appl/Applications/MarkovChain/MarkovChain_9_18/node1.html

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