| 1 | Definition of vector spaces, properties | |
| 2 | Subspaces, sums and direct sums | |
| 3 | Span, independence, bases | |
| 4 | Bases and dimension | Problem set 1 due |
| 5 | Linear maps, null space / range | |
| 6 | matrices, invertibility | Problem set 2 due |
| 7 | Exam 1 on Chapters 1–3 |
| 8 | Finite fields. Systems of equations. | |
| 9 | Gaussian elimination | |
| 10 | Counting over Fp. Invariant subspaces. | Problem set 3 due |
| 11 | Finding eigenvectors | |
| 12 | Upper triangular and diagonal matrices | Problem set 4 due |
| 13 | Eigen vectors over R and Fp
| Problem set 5 due |
| 14 | Exam 2 on Chapters 1–5 |
| 15 | Inner products, Gram-Schmidt | |
| 16 | Orthogonal projection, minimization | |
| 17 | Adjoint, self-adjoint, normal | Problem set 6 due |
| 18 | Spectral theorem | |
| 19 | Positive operators | Problem set 7 due |
| 20 | Isometries, polar decomposition | |
| 21 | Exam 3 on Chapters 1–7 |
| 22 | Generalized eigenspaces | |
| 23 | Generalized eigenspace decomposition | Problem set 8 due |
| 24 | Characteristic polynomial | Problem set 9 due |
| 25 | Determinant | |
| 26 | Trace, canonical commutation relations | |
| | Final Exam |
