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# Linear Algebra

The three midterm exams will be held in Walker during lecture hours
(closed book). All grading questions should go to your recitation instructor!

 W 2/4 The Geometry of Linear Equations 1.1-2.1 F 2/6 Elimination, Matrix Operations 2.2, 2.4 M 2/9 Elimination Matrices and Matrix Inverses 2.3, 2.5 W 2/11 A = LU Factorization 2.6 F 2/13 Permutations, Dot Products, and Transposes 2.7 M 2/16 HOLIDAY (lecture on Tuesday) T 2/17 Vector Spaces and Subspaces 3.1 W 2/18 The Nullspace: Solving Ax = 0 3.2 F 2/20 Solving Ax = b for nonsquare A, Row-reduced Echelon Form 3.3-3.4 M 2/23 Independence, Dimension, and Bases 3.5 W 2/25 The Four Fundamental Subspaces 3.6 F 2/27 Subspaces and Matrix Operations M 3/2 Exam 1: Chapters 1 to 3.4 W 3/4 Graphs and Networks 8.2 F 3/6 Orthogonality and Subspaces (Add Date) 4.1 M 3/9 Projections 4.2 W 3/11 Least Squares Approximations 4.3 F 3/13 Orthonormal Bases, Gram-Schmidt, and A = QR 4.4 M 3/16 Fourier Series and Orthogonal Polynomials 8.5 W 3/18 Properties of Determinants 5.1 F 3/20 Formulas for Determinants; Jacobians 5.2-5.3 M-F 3/23-27 SPRING BREAK M 3/30 Exam Review W 4/1 Exam 2: Chapters 1-5, 8.2, 8.5 F 4/3 Eigenvalues and Eigenvectors 6.1 M 4/6 Similar Matrices, Diagonalization, and Powers of A 6.6, 6.2 W 4/8 Markov Matrices 8.3 F 4/10 Differential Equations 6.3 M 4/13 Symmetric Matrices 6.4 W 4/15 Positive Definite Matrices 6.5 F 4/17 Defective Matrices: Jordan Forms and Generalized Eigenvectors 6.6 M 4/20 HOLIDAY W 4/22 Singular Value Decompositions 6.7 R 4/23 (Drop Date) F 4/24 Matrices in Engineering 8.1 M 4/27 Linear Operators on Functions W 4/29 Exam Review F 5/1 Exam 3: Chapters 1-8 (8.1, 2, 3, 5) M 5/4 Google PageRank; Principal Components Analysis W 5/6 Sparse Matrices and Iterative Methods 9.3 F 5/8 Numerical Linear Algebra 9.1-9.2 M 5/11 Complex Matrices and FFTs 10.1-3 W 5/13 Course Review M-F 5/18-22 Final Exams