Jan Draisma
Professor of Mathematics
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3 November 2025: Schläfli
lecture by Kathlén Kohn.
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Teaching
Linear and Bilinear Algebra
This site contains information about the course Linear and Bilinear
Algebra. The first half of the course we will use lecture notes by Arjeh
Cohen, the following 30 percent we will treat material a book by Babai
and Frankl about linear algebra methods in combinatorics, and the last
20 percent is devoted to other fun applications. To get credit points
you need to hand in homework every week and, at the end, to write a text
about one of the later chapters, or about an article. So far we have done:
- Week 1 (31 August and 1 September): Chapter 1 of lecture notes.
Homework: Exercise 1.7 + Find an invertible 2-by-2 matrix over Z/13Z
of order 7.
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- Week 2 (7 and 8 September): Chapter 2, sections 1 and 2.
eomework: Exercise 2.5 and the exercise in this document,
which also gives a clean definition of extension of scalars.
- Week 3 (14 and 15 September): Chapter 2, sections 3 and 4.
Homework: Exercise 2.9 and this extra exercise.
- Week 4 (21 and 22 September): Chapter 2, rational Jordan normal
form. Homework: Exercise 2.19 and this extra exercise.
- Week 7 (12 and 13 October): Tensor products, Kronecker products, etc.
Homework: Excercise 3.11.
- Week 8 (19 and 20 October): Tensor rank.
Homework: this exercise.
- Week 9 (9 and 10 November): Bilinear forms.
Homework: these exercises.
- Week 10 (16 and 17 November): Sesquilinear forms.
Homework: these exercises.
- Week 11 (23 and 24 November): Orthogonal, symplectic, unitary groups;
exterior powers of spaces and of maps.
Homework: these exercises.
- Week 12 (30 November and 1 December): Bollobás's theorem with
Lovász's proof.
- Week 13 (7 and 8 December): Perron-Frobenius.
Homework: these exercises.
- Week 14 (4 and 5 January): Two linear algebra proofs in combinatorics.
Homework: this exercise.
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