Lecture1 | The Geometry of Linear Equations

Lecture2 | Elimination with Matrices

Lecture3 | Multiplication and Inverse Matrices

Lecture4 | Factorization into A=LU

Lecture5 | Transposes, Permutations, Spaces $R^N$

Lecture6 | Column Space & Nullspace

Lecture7 | Solving Ax=0: Pivot Variables, Special Solutions

Lecture8 | Row Reduced Form R

Lecture9 | Independence, Basis, and Dimension

Lecture10 | The Four Fundamental Subspaces

Lecture11 | Matrix Spaces; Rank1; Small World Graphs

Lecture12 | Graph, Networks, Incidence Matrices

Lecture14 | Orthogonal Vectors and Subspaces

Lecture15 | Projections onto Subspaces

Lecture16 | Projection Matrices and Least Squares

Lecture17 | Orthogonal Matrices and Gram-Schmidt

Lecture18 | Properties of Determinants

Lecture19 | Determinant Formulas and Cofactors

Lecture20 | Cramer’s Rule, Inverse Matrix and Volume

Lecture21 | Eigenvalues and Eigenvectors