4 Drawing Vector
5 Dot Products9 Vector Space Dimensions
10 Matrices, Addition and Scalar Multiplication11 Matrix Multiplication
12 Fundamental Question: \(A\overrightarrow{v} = \overrightarrow{b}\)16 Elimination and Factorization
17 Transpositions and Permutations
18 Vector Spaces and Subspaces
19 The Nullspace of a Matrix
20 The Rank and Row Reduced Form
21 Solutions to \(Ax = b\)
22 Independence, Basis, and Dimension
23 Dimension of the Four Subspaces
24 Orthogonality
25 Projections
26 Least Square Approximations
27 Orthogonal Bases and Gram-Schmidt
28 Determinants
29 Permutations and Cofactors
30 Cramer's Rule
31 Eigenvalues and Eigenvectors32 Diagonalizing a Matrix
33 Symmetric Matrices
34 Positive Definite and Positive Semi-Definite