Course Calendar
Course Lessons
| Lsn # | Lesson | Suggested Problems | Section | Video |
| 1 | 1 Introduction to Course / Vectors | 1,2,9,12,28 // 4,7,10,29,33 | § 1.1,1.2 | |
| 2 | 2 Matrices / The Geometry of Linear Equations | 1,2,3,4 // 1,2,3,4,5,9,11,12,13,33 | § 1.3, 2.1 | 1 |
| 3 | 3 Matrix Elimination | 1,2,3,4,5,11,12,25 | § 2.2 | 2 |
| 4 | 4 Elimination with Matrices | 1,2,3,12,14,16,17,24,25,26,27 | § 2.3 | 2 |
| 5 | 5 Matrix Operations and Inverses | 1,2,3,4,5,14,15,29,30,32 // 1,2,7,8,10,15,23,28,29,32 | § 2.4, 2.5 | 3 |
| 6 | 6 Factorization LU and LDU | 5,6,7,12,15,16 | § 2.6 | 4 |
| 7 | 7 Transposes and Permutations | 1,2,4,5,8,11,12,22,30 | § 2.7 | 5 |
| 8 | 8 Vector Spaces and Subspaces | 1,2,10,12,13,15,16,19,20,22,23,26,27,29 | § 3.1 | 6 |
| 9 | 9 Nullspace of A | 1,2,3,4,5,15,17,24,33,34 | § 3.2 | 7 |
| 10 | 10 Complete Solution Ax=b | 1,2,3,4,5,6,16,18,19,26,28,31,34 | § 3.3 | 8 |
| 11 | 11 Independence, Basis, Dimension | 1,3,5,9,11,13,15,21,24 | § 3.4 | 9 |
| 12 | 12 Independence, Basis, Dimension | 2,4,6,10,12,16,18,20 | § 3.4 | 9 |
| 13 | 13 Four Fundamental Subspaces | 1,3,7,11,13,19,25,26 | § 3.5 | 10 |
| 14 | 14 Four Fundamental Subspaces / Review | 2,4,6,8,12,14,18,24 | § 3.5 | 10 |
| 15 | 15 Written Partial Review #1 | Review Lessons 1-14 | Chapters 1-3 | 13 |
| 16 | 16 Orthogonality - Four Fundamental Subspaces | 1,2,3,4,5,6,8,10a,11,12,13,21,27,28 | § 4.1 | 14 |
| 17 | 17 Projections | 1,2,3,5,6,7,8,11,13,17,19,21 | § 4.2 | 15 |
| 18 | 18 Least Squares Approximations | 1,2,3,4,6,7,8,9,10,17,18 | § 4.3 | 16 |
| 19 | 19 Orthonormal Basis and Gram-Schmidt | 1,2,4,5,17,18,19,21,22,24 | § 4.4 | 17 |
| 20 | 20 Properties of Determinants | 1,2,3,4,5,6,9,12,13,14,22,23,28 | § 5.1 | 18 |
| 21 | 21 Formula for Determinants | 1,2,3,4,11,12,13 | § 5.2 | 19 |
| 22 | 22 Applications of Determinants | 1,2,3,6,8,16,17,18 | § 5.3 | 20 |
| 23 | 23 Written Partial Review #2 | Chapters 4-5 | ||
| 24 | 24 Eigenvalues and Eigenvectors | 2,3,4,5,6,7,8,29,32 | § 6.1 | 21 |
| 25 | 25 Diagonalization | 1,2,3,4,6,7,11,12,13,15,16,17 | § 6.2 | 22 |
| 26 | 26 Systems of Differential Equations | 1,3,4,5,8,10,18,24 | § 6.3 | 23 |
| 27 | 27 Symmetric Matrices | 1,6,7,9,23,26 | § 6.4 | 25 |
| 28 | 28 Positive Definite Matrices | 1,2,3,4,5,7,8,9,11,29,31 | § 6.5 | 27,28 |
| 29 | 29 Singular Value Decomposition | 6,7 // 1,2,4,5,8,9,15 | § 7.1, 7.2 | 29 |
| 30 | 30 Linear Transformations | 1,2,3,8,11,12,13,20,21,22 | § 8.1 | 30 |
| 31 | 31 Matrix of a Linear Transformation | 1,5,6,7,10,11,12,14,15,19 | § 8.2 | 31 |
| 32 | 32 Principal Component Analysis | 1,2,4,5,8,9,15 | § 7.3 | 32 |
| 33 | 33 Geometry of Principal Component Analysis | 1,2,5,6 // data problem | § 7.4 | 33 |
| 34 | 34 Review / Course Project Intro | Chapters 6-8 | 34 | |
| 35 | 35 Written Partial Review #3 | Chapters 6-8 | ||
| 36 | 36 Application: Graphs and Networks | 1,2,3,4,5,8,9,10,11,12 | § 10.1 | 12 |
| 37 | 37 Application: Markov Matrices, Population Models | 1,2,3,5,7,12,13 | § 10.3 | 24 |
| 38 | 38 Application: Linear Programming | 1,2,3,4,5 | § 10.4 | |
| 39 | 39 Project Due - West Point Writing Program | Course Project | ||
| 40 | 40 Course Review | Chapters 1-8, 10 | 36 |