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Linear Algebra

Constructor University, Spring 2026

Official Class Description from Campusnet

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:

• Vector spaces
• Linear Operators
• Dual spaces
• Isomorphisms
• Connection to matrices
• Sums and direct sums
• Fundamental spaces of a linear operator
• Diagonalization of linear operators (on finite dimensional spaces)
• Cayley-Hamilton theorem
• Jordan decomposition
• Jordan normal form and its applications to linear differential equations
• Decomplexification and complexification
• Bilinear Forms and their classification
• Quadratic forms and orthogonalization
• Euclidean and unitary spaces
• Orthogonal and unitary operators
• Self-adjoint operators

News

• First tutorial is on Wed., Feb. 4, 2026, 11:15, in Res. I LH.
• First class is on Mon., Feb. 2, 2026, 8:15, in Res. I LH.

Contact Information

Time and Place

Textbooks

The class material is similar to the following textbooks:

• A. I. Kostrikin and Y. I. Manin - Linear Algebra and Geometry (Gordon and Breach Science Publishers). This class covers parts of Chapters 1 and 2.
• S. Axler - Linear Algebra Done Right (Springer, third edition).

Extra Material

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)

Grading

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

Exams

There will be one final exam (centrally scheduled in May) and one make-up final exam (centrally scheduled in August).

Homework Exercises

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

• The two worst homework sheets are not considered for grading.
• It is encouraged to discuss the homework sheets with your classmates (e.g., discuss how to come up with the solution or what the right way of approaching the problem is). On the other hand, the solutions must be written down and handed in individually! Copying the solutions from somebody else is a violation of Academic Integrity.

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

Class Schedule

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).