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