Introduction to Linear AlgebraMAT 211 (LEC 3)Spring 2009 |
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Mathematics department | |
Julia Viro |
Generalities | Instructors | Schedule | Homework | Exams | Help |
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Day of | Contents | Sections |
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1/27, 1/29 | Linear systems and their geometric interpretation. Matrices and vectors. The matrix form of a linear system. Gauss-Jordan elimination. | 1.1-1.2 |
2/3, 2/5 | Matrix vocabulary. Operations on matrices. Space Rn. Rank of a matrix. Number of solutions of a linear system. | 1.2-1.3 |
2/10, 2/12 | 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 |
2/17, 2/19 | Subspaces of Rn. Linear combinations of vectors. Span of vectors. Linear dependence and independence. Basis. Coordinates. Dimension. | 3.1-3.4 |
2/24, 2/26 | Kernel and image of a linear transformation. Kernel- Image (Rank-Nullity) theorem. | 3.3 |
3/3 | Review for Midterm I. | 1.1-3.4 |
Thursday 3/5 | Midterm I | |
3/10, 3/12 | Linear transformations and their matrices. Isomorphisms. Change of a basis. | 4.2-4.3 |
3/17, 3/19 | Inner product spaces. Euclidean space Rn. Orthogonality. Orthonormal bases. Orthogonal projections. Orthogonal complement. | 5.1 |
3/23-3/27 | Cauchy-Schwarz inequality, triangle inequality. Gram-Schmidt orthogonalization and QR-factorization.Orthogonal transformations and orthogonal matrices. | 5.2-5.3, 5.5 |
3/31 | Review for Midterm II. | 4.1-4.3, 5.1-5.3, 5.5 |
Thursday 4/2 | Midterm II | 4.1-4.3, 5.1-5.3, 5.5 |
4/6-4/10 | Spring recess | |
4/14, 4/16 | Determinants and their geometrical interpretation. Properties of determinants. | 6.1-6.3 |
4/21, 4/23 | Eigenvalues and eigenvectors. Eigenspaces. | 7.1-7.3 |
4/28, 4/30 | Characteristic equation. Algebraic and geometric multiplicity of an eigenvalue. Eigenbasis. Diagonalization. | 7.4 |
5/5, 5/7 | Review for Final. | |
Tuesday 5/12 12:00-1:30 in P131 (Math Tower) |
Extra review for Final | |
Tuesday 5/19 11:00am-1:30pm |
Final exam |