Unit 5 · Eigenvalues and Dynamics

Chapter 5.2

Markov Matrices and Difference Equations

A population shuffles between states, step after step. For a regular Markov matrix the eigenvalue 1 holds the steady state, and the size of the second-largest eigenvalue sets how fast everything else fades.

11–15 min · in preparation · lesson 14 of 21

By the end

  1. 01Identify Markov matrices and their eigenvalue structure
  2. 02Solve difference equations u_{k+1} = Au_k by eigenvector expansion
  3. 03Find and interpret steady states

In unit 5

  1. 5.1Eigenvalues and Diagonalization13–16
  2. 5.2Markov Matrices and Difference Equations11–15
  3. 5.3Differential Equations and the Matrix Exponential11–15
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