| Date | Topic | Section | Problem Sets | Solutions | |
| Lecture 1 | Jan 13 | Logistics, Vector spaces (an informal discussion) | 1.1 | Problem Set 1 | Problem Set 1 Solutions |
| Lecture 2 | Jan 15 | Vector spaces | 1.2 | ||
| Lecture 3 | Jan 17 | Linear subspaces | 1.3 | ||
| Lecture 4 | 1/22 | Linear combinations and generating sets | 1.4 | Problem Set 2 | Problem Set 2 Solutions |
| Lecture 5 | Jan 24 | Basis I | 1.5 | ||
| Lecture 6 | Jan 27 | Basis II | 1.6 | Problem Set 3 | Problem Set 3 Solutions |
| Lecture 7 | Jan 29 | Linear Transformations, Kernel and Image | 2.1 | ||
| Lecture 8 | Jan 31 | Dimension Theorem | 2.1 | ||
| Lecture 9 | Feb 3 | Matrix representation of linear transformations | 2.2 | Problem Set 4 | Problem Set 4 Solutions |
| Lecture 10 | Feb 5 | Composition of linear transformations, multiplication of matrices | 2.3 | ||
| Lecture 11 | Feb 7 | Invertible linear transformations | 2.4 | ||
| Lecture 12 | Feb 10 | Change of coordinate matrices | 2.5 | Midterm I | Midterm I Solutions |
| Midterm I | Feb 12 | NA | NA | ||
| Lecture 13 | Feb 14 | Change of coordinate matrices, invertible matrices | 2.5 | Take-Home Exam I | |
| Lecture 14 | Feb 17 | Systems of linear equations, elementary row operations | 3.1, 3.3, 3.4 | Problem Set 5 | |
| Lecture 15 | Feb 19 | Systems of linear equations, reduced row echelon form | 3.1, 3.4 | ||
| Lecture 16 | Feb 21 | Reduced row echelon form and Gaussian elimination | 3.4 | ||
| Lecture 17 | Feb 24 | Image and RREF, column operations | 3.1, 3.4 | Problem Set 6 | |
| Lecture 18 | Feb 26 | Rank, row space and column space | 3.2 | ||
| Lecture 19 | Feb 28 | Rank and inverse of matrices | 3.2, 3.4 | ||
| Lecture 20 | March 2 | Determinant I | 4.1, 4.2, 4.3 | Problem Set 7 | |
| Lecture 21 | March 4 | Determinant II | 4.1, 4.2, 4.3 | ||
| Lecture 22 | March 6 | Determinant III | 4.1, 4.2, 4.3 | ||
| Lecture 23 | March 23 | Determinant III | 4.1, 4.2, 4.3 | Problem Set 8 | |
| Lecture 24 | March 25 | Eigenvalues and eigenvectors | 5.1 | ||
| Lecture 25 | March 27 | Diagonalization I | 5.2 | ||
| Lecture 26 | March 30 | Diagonalization II | 5.2 | Take-Home Exam II | |
| Lecture 27 | April 1 | Diagonalization III | 5.2 | ||
| Lecture 28 | April 3 | T-invariant subspaces | 5.3 | ||
| Lecture 29 | April 6 | Cayley-Hamilton Theorem | 5.3 | Problem Set 9 | |
| Lecture 30 | April 8 | Inner product spaces | 6.1 | ||
| Lecture 31 | April 10 | Cauchy-Schwartz inequality and orthogonal sets | 6.1 | ||
| Lecture 32 | April 13 | Orthonormal bases | 6.2 | Problem Set 10 | |
| Lecture 33 | April 15 | Orthogonal complements | 6.2 | ||
| Lecture 34 | April 17 | Adjoint of linear transformations I | 6.3 | ||
| Lecture 35 | April 20 | Adjoint of linear transformations II | 6.3 | ||
| Lecture 36 | April 22 | Normal operators | 6.4 | ||
| Lecture 37 | April 24 | Orthogonal and Hermitian operators | 6.4, 6.5 |