Unit 5 · Eigenvalues and Dynamics

Chapter 5.1

Eigenvalues and Diagonalization

Some vectors keep their direction when A acts — and they crack the matrix open: A = SΛS⁻¹ turns matrix powers into scalar powers.

13–16 min · in preparation · lesson 13 of 21

By the end

  1. 01Compute eigenvalues via det(A − λI) = 0 and their eigenvectors
  2. 02Diagonalize a matrix when possible and explain when it is not
  3. 03Use diagonalization to compute Aᵏ

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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