Linear Algebra › Section E · Eigenvalues and eigenvectors › Topic E.6
Discrete dynamical systems
Populations, markets and networks are often modelled one time step at a time, with a matrix carrying this year's state to next year's. Eigenvalues and eigenvectors predict where such a system ends up: whether it grows, dies out or settles, and in what proportions.
In this topic
- Systems that move in steps
- The eigenvector decomposition
- Worked example: a two-stage population
- Reading the long run
- Age-structured population models
- Pictures in the plane: attractors, repellers, saddles
- Worked example: a saddle point
- Changing variables to decouple
- Complex eigenvalues: spirals
- Ranking web pages
- Common mistakes to avoid
- Key takeaways
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