Week of |
Contents |
Sections |
1/26 |
Linear systems and their geometric interpretation. Matrices and vectors. The matrix form of a linear system. Gauss-Jordan elimination. |
1.1-1.2 |
2/2 |
Matrix vocabulary. Operations on matrices. Space Rn. Rank of a matrix. Number of solutions of a linear system. |
1.2-1.3 |
2/9-2/16 |
Linear transformations from Rm to Rn. Matrix of a linear transformation. Linear transformations in a plane: scalings, projections, reflections, rotations, shears. Composition of linear transformations and matrix product. Inverse linear transformation and invertible matrices. |
2.1-2.4 |
2/23 |
Subspaces of Rn. Linear combinations of vectors. Span of vectors. Linear dependence and independence. Basis. Coordinates. Dimension. |
3.1-3.4 |
3/2 |
Kernel and image of a linear transformation. Kernel- Image (Rank-Nullity) theorem. | 3.3 |
3/9 |
Midterm I on 3/9;
Kernel- Image (Rank-Nullity) theorem. | 3.3 |
3/16 |
Linear transformations and their matrices. Change of a basis. | 3.4 |
3/22 |
Linear spaces. Linear transformations and their matrices. Isomorphisms. | 4.1-4.2 |
3/30 |
Inner product spaces. Euclidean space Rn. Orthogonality. |
5.1 |
4/6 | Spring break |
|
4/13 |
Orthogonal projections.
Orthogonal complement. Cauchy-Schwarz inequality, Pythagorean Theorem.
Gram-Schmidt orthogonalization. General inner product spaces. | 5.1 -5.2, some of 5.5 |
4/20 |
Midterm II on Apr 20; Determinants. |
6.1 |
4/27 |
Determinants and their geometrical interpretation. Properties of determinants. |
6.1-6.3 |
5/4 |
Eigenvalues and eigenvectors. Eigenspaces. Characteristic equation. Eigenbasis. Diagonalization. |
7.1-7.4 |
Friday 5/15 11:00-1:30 |
Final exam
| |
|