Topics

• Introduction to Vectors

  • Vectors and Linear Combinations

  • Length and Dot Products

  • Matrices

• Solving Linear Equations

  • Vectors and Linear Equations

  • Idea of Elimination

  • Elimination Using Matrices

  • Rules for Matrix Operations

  • Inverse Matrices

  • Transposes and Permutations

• Vector Spaces and Subspaces

  • Spaces of Vectors

  • Nullspace of a matrix

  • Complete solution of a system of equation

  • Independence, Basis and Dimensions

  • Dimensions of the Four Subspaces

• Orthogonality

  • Orthogonality of the Dour Subspaces

  • Projections

  • Least Squares Approximations

• Determinants

  • Properties of Determinants

  • Permutations and Cofactors

• Eigenvalues and Eigenvectors

  • Introductions to Eigenvalues

  • Diagonalizing a matrix

  • Symmetric matrices

  • Positive Definite matrices

• Singular Value Decomposition

  • Bases and matrices