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