Matrix models.
Use matrices to organise networks, predict changes and evaluate practical models.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Matrix arithmetic revision
Use matrix order, entries and row-by-column multiplication to organise and calculate with data.
- 02
Network/adjacency matrices
Represent a network in an adjacency matrix and recover its connections.
- 03
Powers and numbers of connections
Use adjacency powers to count walks of a specified number of steps.
- 04
Reachability and dominance/ranking applications
Investigate reachability and transparent rule-based dominance rankings.
- 05
Transition matrices and state vectors
Build a column-stochastic transition matrix and use it to update a state vector.
- 06
Repeated transitions
Predict repeated transitions using matrix powers and the correct time order.
- 07
Long-term behaviour and steady states
Solve a steady-state equation and distinguish a fixed distribution from convergence.
- 08
Closed-system assumptions and model limitations
Evaluate matrix models using their assumptions, totals and independent observations.
Topic review
Revisit the key ideas, then choose a practice paper.