Constructor University, Spring 2026
This module continues the introduction to Linear Algebra from the methods module "Matrix Algebra and Advanced Calculus I". The fundamental concepts and techniques of Linear Algebra are introduced in a rigorous and more abstract way. The first half of this module covers vector spaces and linear maps, while the second half covers inner products and geometry. The following topics will be covered:
The class material is similar to the following textbooks:
Please note that this class follows the 2018 edition, with some smaller changes and some updates. The corresponding website with lecture notes can be found here: Linear Algebra (Fall 2018)
The grade is only based on the final exam. Homework submissions can provide up to 10% bonus points according to the following table:
| HW percentage solved (rounded up) | Bonus percentage |
|---|---|
| 91 - 100 | 10 |
| 81 - 90 | 9 |
| 71 - 80 | 8 |
| 61 - 70 | 7 |
| 51 - 60 | 6 |
| 41 - 50 | 5 |
| 31 - 40 | 4 |
| 21 - 30 | 3 |
| 11 - 20 | 2 |
| 1 - 10 | 1 |
| less than 1 | 0 |
There will be one final exam (centrally scheduled in May) and one make-up final exam (centrally scheduled in August).
Each week on Monday (with some exceptions) there will be a homework assignment. These are an integral part of the coursework and working on the exercise sheets consistently is the best preparation for the exams. Note that
| Date | Sheet Number | Due Date |
|---|---|---|
| Feb. 02, 2026 | Sheet 1 | Feb. 11, 2026 |
| Feb. 09, 2026 | Sheet 2 | Feb. 18, 2026 |
| Feb. 16, 2026 | Sheet 3 | Feb. 25, 2026 |
| Feb. 23, 2026 | Sheet 4 (corrected) | Mar. 04, 2026 |
| Mar. 02, 2026 | Sheet 5 | Mar. 11, 2026 |
| Mar. 09, 2026 | Sheet 6 | Mar. 18, 2026 |
| Mar. 16, 2026 | Sheet 7 | Mar. 25, 2026 |
| Mar. 23, 2026 | Sheet 8 | Apr. 15, 2026 |
Will be updated while class is progressing.
(Note that the book references given below offer only a rough orientation. Sometimes, only parts of a particular chapter are covered in class.)
| Date | Topics |
|---|---|
| Feb. 02, 2026 | Fields, vector spaces, subspace, span Kostrikin/Manin Ch. 1 §1; Axler (third edition) Ch. 1.A, 1.B, 1.C, 2.A |
| Feb. 09, 2026 | Subspace, span, basis, dimension parts of Kostrikin/Manin Ch. 1 §2; Axler Ch. 1.C, 2.A, 2.B, 2.C |
| Feb. 16, 2026 | Zorn's lemma, linear operators, dual space Kostrikin/Manin Ch. 1 §1.9, §2.17-2.20 and §3.1-3.5; Axler Ch. 3.A and beginning of 3.F |
| Feb. 23, 2026 | Isomorphisms, dual map, kernel, image and dimension Kostrikin/Manin Ch. 1 §3.6-3.11 and §7.4; Axler Ch. 3.B, beginning of Ch. 3.D, parts of Ch. 3.F (3.99-3.101). |
| Mar. 02, 2026 | Kernel, image and dimension, rank-nullity theorem, matrices, sums and direct sums Kostrikin/Manin Ch. 1 §3.11-3.13,§4.4-4.9, §5.2-5.3. Axler Ch. 3.B, Ch. 3.C, the matrix parts of Ch. 3.D, Ch. 1.C, and 2.43 in Ch. 2.C; if you like you can also look around in Axler Ch. 10 a bit to get more background on the trace and determinant (most of which should be familiar to you) |
| Mar. 09, 2026 | Sums, direct sums, quotient spaces, fundamental spaces of a linear operator Kostrikin/Manin Ch. 1 §5 and §6; Axler parts of Ch. 3.E |
| Mar. 16, 2026 | Fundamental spaces of a linear operator; Linear operators on finite dimensional spaces (diagonalizability, characteristic polynomial) Kostrikin/Manin Ch. 1 §6.10 and §7.6, and §8.1-8.5. Axler parts of Ch. 3.F, and parts of Ch. 5 (covers much of the same topics in a slightly different way). |
| Mar. 23, 2026 | Diagonalizability, Cayley-Hamilton, generalized eigenspaces Kostrikin/Manin Ch. 1 §8 (most parts); Axler Ch. 8.C (Axler proves the abstract Jordan decomposition first and uses it to prove Cayley-Hamilton) |