### Session Overview

Like differential equations, Markov matrices describe changes over time. Once again, the eigenvalues and eigenvectors describe the long term behavior of the system. In this session we also learn about Fourier series, which describe periodic functions as points in an infinite dimensional vector space. |

### Session Activities

#### Lecture Video and Summary

- Watch the video lecture Lecture 24: Markov Matrices; Fourier Series
- Read the accompanying lecture summary (PDF)
- Lecture video transcript (PDF)

#### Suggested Reading

- Read Section 8.3 and 8.5 in the 4
^{th}edition or Sections 10.3 and 10.5 in the 5^{th}edition.

#### Problem Solving Video

- Watch the recitation video on Problem Solving: Markov Matrices
- Recitation video transcript (PDF)

### Check Yourself

#### Problems and Solutions

Work the problems on your own and check your answers when you’re done.