5.1 Two-by-Two Matrices: Introduction
  5.1.1 Linear Equations of Two Unknowns
  5.1.2 Two–by–Two Matrices: Definition
  5.1.3 Linear Mappings and Matrix Operatings
 5.2 Two–by–Two Matrices: Linear Mappings
  5.2.1 Specific Linear Mappings 1: the Unit Matrix
  5.2.2 Specific Linear Mappings 2: Stretching and Shrinking
  5.2.3 Specific Linear Mappings 3: Projections
  5.2.4 Specific Linear Mappings 4: Rotations
  5.2.5 Specific Linear Mappings 5: Reflections
 5.3 Two–by–Two Matrices: Index Notation and Multiplication
  5.3.1 Basis Vectors and Index Notation
  5.3.2 Multiplication of a Matrix with a Scalar
  5.3.3 Matrix Multiplication: Definition
  5.3.4 Matrix Multiplication: Index Notation
 5.4 Inverse of a Matrix
  5.4.1 Motivation
  5.4.2 Definition and Theorem
 5.5 Eigenvalues and eigenvectors
  5.5.1 A physics example