Markov Chains MADE EASY | Linear Algebra APPLICATIONS
In this video, we cover linear algebra applications. We show how eigenvalues and eigenvector can be used to determine steady states of Markov chains. We discuss probability vectors and transition matrices, which are stochastic matrices. We prove that every stochastic matrix has 1 as its eigenvalue.
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CHAPTERS:
0:00 A simple example of a Markov chain: changing weather
3:11 Transition matrix of a Markov chain
5:00 Probability vectors and stochastic matrices
6:00 Eigenvalues of stochastic matrices
7:37 Steady-state vectors
8:26 How to find a steady-state vector
9:54 Long-term behavior of a Markov chain
10:25 Steady states might not be reachable
11:01 Regular transition matrices and steady states
12:10 Your homework assignment
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