Linear Algebra › Section D · Vector spaces › Topic D.9
Markov chains
A Markov chain follows a system that moves at random between states, where only the present state affects the next step. Its long-run behaviour is found by solving one homogeneous linear system.
In this topic
- Random moves, linear algebra
- Probability vectors and stochastic matrices
- The chain as a recurrence
- Worked example: two coffee shops
- Steady-state vectors
- Worked example: the coffee shops in the long run
- Regular matrices and convergence
- Worked example: three weather states
- When there is no convergence
- Common mistakes to avoid
- Key takeaways
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