Linear Algebra: Math 254, Fall 2009
Schedule



Textbook: Lay, Linear Algebra and Its Applications 3rd ed.

Schedule

My best approximation.

Day Topics Preparation
Mon. 8/31 Introduction.
Solution of a 2 by 2 system in excruciating detail.
Sec. 1.1-2
Wed. 9/2 Solution and geometry of 3 by 3 systems.
Reduced Row Echelon Form (RREF).
Sec. 1.2
Fri. 9/4 Vectors: scalar products and sums.
Gaussian elimination: final words.
Sec. 1.3
Wed. 9/9 The span of a set of vectors. Sec. 1.3-4
Fri. 9/11 Matrix equations. Sec. 1.4
Mon. 9/14 Matrix equations.
A traffic problem leading to a linear system.
Sec. 1.5-6
Wed. 9/16 Linear independence. Sec. 1.7
Fri. 9/18 Linear transformations. Sec. 1.8-9
Mon. 9/21 Linear transformations. Sec. 1.8-9
Wed. 9/23 Matrix multiplication. Sec. 2.1
Fri. 9/25 The inverse of a matrix. Sec. 2.2
Mon. 9/28 Invertible matrices: key concepts. Sec. 2.3
Wed. 9/30 The Invertible Matrix Theorem
Determinants .
Sec. 2.3
3.1
Fri. 10/2 Determinants. Sec. 3.1-2
Mon. 10/5 Exam. Sec. 1.1-9, 2.1-3
Wed. 10/7 Properties of determinants Sec. 3.1-2
Fri. 10/9 Cramer's rule, volume. Sec. 3.3
Mon. 10/12 Fields, vector spaces.
Subspaces, column space of a matrix.
Sec. 4.1
Wed. 10/14 Nullspace of a matrix.
Kernel of a linear transformation.
Sec. 4.2
Fri. 10/16 Basis of a vector space. Sec. 4.3
Mon. 10/19 Coordinate systems. Sec. 4.4
Wed. 10/21 The basis theorem. Sec. 4.5
Fri. 10/23 The rank theorem.
Linear recursion.
Sec. 4.6,8
Mon. 10/26 Change of basis. Sec. 4.7
Wed. 10/28 Change of basis. Sec. 4.7
Fri. 10/30 Markov chains and predicting the future! Sec. 4.9.
Mon. 11/2 Exam. Ch. 3.1-3, Ch. 4.1-7
Wed. 11/4 Two population problems. Sec. 5.1
Fri. 11/6 Eigenvalues and eigenvectors. Sec. 5.1-2
Mon. 11/9 Diagonalization. Sec. 5.3
Fri. 11/13 Diagonalization and linear transformations. Sec. 5.4
Mon. 11/16 Complex eigenvalues. Sec. 5.5
Wed. 11/18 Discrete dynamical systems. Sec. 5.6
Fri. 11/20 . .
Mon. 11/23 EXAM. Sec. 4.4-7; 4.9; 5.1-6
Mon. 11/30 Inner product and orthogonality. Sec. 6.1
Wed. 12/2 Orthogonal projection and orthonormal basis. Sec. 6.2
Fri. 12/4 Geometry of orthogonal projections. Sec. 6.3
Mon. 12/7 Gram-Schmidt and QR factorization. Sec. 6.4
Wed. 12/9 Least squares problems. Sec. 6.5
Fri. 12/11 .. .