| Day of | Contents | Sections |
|---|---|---|
| 1/29, 1/31 | Linear systems and their geometric interpretation. Matrices and vectors. The matrix form of a linear system. Gauss-Jordan elimination. | 1.1-1.2 |
| 2/5, 2/7 | Matrix vocabulary. Operations on matrices. Space Rn. Rank of a matrix. Number of solutions of a linear system. | 1.2-1.3 |
| 2/12, 2/14 | Linear transformations from Rm to Rn. Matrix of a linear transformation. Linear transformations in a plane: scalings, projections, reflections, rotations, shears. | 2.1-2.2 |
| 2/19, 2/21 | Composition of linear transformations and matrix product. Inverse linear transformation and invertible matrices. | 2.3-2.4 |
| 2/26, 2/28 | Subspaces of Rn. Linear combinations of vectors. Span of vectors. Linear dependence and independence. Basis. Coordinates. Dimension. Kernel and image of a linear transformation. Kernel- Image (Rank-Nullity) theorem. | 3.1-3.3 |
| 3/4 | Review for Midterm I. | 1.1-3.4 |
| 3/6 | Midterm I | 1.1-3.4 |
| 3/11, 3/13 | Change of a basis. Similar matrices. Definition of a linear space. A subspace of a linear space. Linear combinations, span, linear dependence and independence, basis, coordinates, dimension. | 4.1 |
| 3/17-3/22 | Spring Recess | |
| 3/25, 3/27 | Linear transformations and their matrices. Isomorphisms. Change of a basis. | 4.2-4.3 |
| 4/1, 4/3 | Inner product spaces. Euclidean space Rn. Orthogonality. Orthonormal bases. Orthogonal projections. Orthogonal complement. Cauchy-Schwarz inequality, triangle inequality. Gram-Schmidt orthogonalization and QR-factorization. | 5.1-5.2 |
| 4/8 | Orthogonal transformations and orthogonal matrices. Review for Midterm II. | 5.3, 5.5 |
| 4/10 | Midterm II | 4.1-4.3, 5.1-5.3, 5.5 |
| 4/15, 4/17 | Determinants and their geometrical interpretation. Properties of determinants. | 6.1, 6.3 |
| 4/22, 4/24 | Eigenvalues and eigenvectors. Eigenspaces. | 6.2 |
| 4/29, 5/1 | Characteristic equation. Algebraic and geometric multiplicity of an eigenvalue. | 7.1-7.3 |
| 5/6 | Eigenbasis. Diagonalization. Eigenvalues and eigenvectors of a linear transformation. | 7.4 |
| 5/8 | Review for the Final exam. | |
| 5/15 | Final exam | |