Introduction to Linear Algebra

MAT 211 (LEC 3)

Spring 2009

Mathematics department
Julia Viro

Generalities Instructors Schedule Homework Exams Help

Tentative schedule

Day of Contents Sections
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
4/6-4/10Spring 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

in P131
(Math Tower)
Extra review for Final
Tuesday 5/19
Final exam