• 8.1 Eigenvalues and eigenspace

  • 8.1.1 Eigenvalues and eigenvectors – topics
  • 8.1.2 Eigenvectors and eigenspace – introduction
  • 8.1.3 Eigenvectors and eigenspace – example
  • 8.1.4 Eigenspace
  • 8.1.5 Geometric multiplicity
  • 8.1.6 Characteristic equation
  • 8.1.7 Algebraic multiplicity
  • 8.1.8 Algebraic and geometric multiplicity
  • 8.1.9 Independence of eigenvectors

• 8.2 Similarity

  • 8.2.1 Similarity – definition
  • 8.2.2 Similarity – example

• 8.3 Diagonalization

  • 8.3.1 What is a diagonalization of a matrix
  • 8.3.2 How can we diagonalise a matrix
  • 8.3.3 Diagonalization – example
  • 8.3.4 Geometric versus algebraic multiplicity
  • 8.3.5 When can we diagonalise a matrix?
  • 8.3.6 When can we diagonalise a matrix – examples

• 8.4 Complex eigenvalues

  • 8.4.1 Complex eigenvalues and eigenvectors – introduction
  • 8.4.2 Complex eigenvectors
  • 8.4.3 Complex eigenvectors – example
  • Pen and Paper Exercises – Module 8. Eigenvalues and eigenvectors