Linear Algebra 2 tutorials
Room: N4, Troja Building
Time: Thursday, 12:20 - 13:50
Postal Owl Token: owl.mff.cuni.cz/join/094144cf0549
Room: N2, Troja Building
Time: Thursday, 14:00 - 15:30
Postal Owl Token: owl.mff.cuni.cz/join/d957ff137b23
Lectures by Dr. Petr Kolman
General information: To obtain the course credit, it is necessary to earn at least 120 points out of a total of 240 points awarded throughout the semester. You can get the points for solving tests. There will be four of them for 50+50+50+90=240 points.
Students who have earned at least 100 points by the end of the course may make up the remaining points by completing additional homework assignments or taking an extra written test (according to the instructor's instructions).
In justified cases (long-term illness, stay abroad, etc.), the instructor may set individual conditions for awarding the credit.
The course credit ("zápočet") is a prerequisite for taking the exam.
Any kind of cheating constitutes grounds for withholding the course credit.
Dates of the tests: March 12, April 2, April 30, May 21.
One-two weeks before the tests I will post homeworks in Postal Owl. These homeworks are intended only for preparation to the tests, you will not get any points for them, just my feedbacks.
Below you can find the set of problems with solutions to them (I take some of the problems from this file). It would be good for you to practise on them during your free time.
In case you have any questions regarding material covered during lectures or tutorials (it might be questions not only about Linear Algebra 2), do not hesitate to contact me via email kuznietv@kam.mff.cuni.cz, I am always glad to help you. Just write me your question and we can either make Office Hours or I can answer to you via email.
Tutorial 1 (19.02.2026). Inner product, norm, orthogonality, Cauchy-Schwarz inequality. Exercises. Solutions.
Tutorial 2 (26.02.2026). Orthogonality, Orthonormal basis, Fourier coefficients, Gram-Schmidt orthonormalization. Exercises
Tutorial 3 (05.03.2026). Orthogonality, Orthogonal complement, Least Squares Method. Exercises
Tutorial 4 (12.03.2026). Test. Orthogonal matrices, QR-decomposition. Exercises.
Tutorial 5 (19.03.2026). Determinant. its properties and Cramer’s rule. Exercises.
Tutorial 6 (26.03.2026). Determinant. Inverse Matrix. Laplace Expansion. Eigenvalues and Eigenvectors. Exercises.
Tutorial 7 (02.04.2026). Test. Eigenvalues and Eigenvectors. Characteristic polynomial. Similar, diagonalizable matrices. Exercises.
Tutorial 8 (09.04.2026). Continuation of previous one. Exercises.
Tutorial 9 (16.04.2026). Diagonalizable matrices. Symmetric and Hermitian matrices. Exercises.
Tutorial 10 (23.04.2026). Jordan normal form. Positive definite matrices. Exercises
Tutorial 11 (30.04.2026). Test. Diagonalization. Positive defineteness.
Tutorial 12 (07.05.2026). Positive definite matrcies and their criterions. Exercises.
Tutorial 13 (14.05.2026). Bilinear and quadratic forms. Exercises.
(Final) Tutorial 14 (21.05.2026). Test.
Combinatorics and Graph Theory 1 tutorials
Room: S11, Malostranska building
Time: Wednesday 12:20-13:50, Thursday 15:40-17:10
Lectures by Josef "Pepa" Tkadlec
Credit requirements: To get a credit you need to obtain at least 100 points out of 150 possible. Points can be obtained via:
Tests: there will be three, each worth 50 points on:
21-22 October
25-26 November
16-17 December.
Only the best 2 tests count. It will contain problems similar to what we cover on tutorials.
Homeworks: Every Friday I will publish 1 problem on Postal Owl (enroll link: owl.mff.cuni.cz/join/1016bfaee611, token: 1016bfaee611) with 1 week deadline. Points for each homework may vary, but for completing all of them you can get 50 points. To get full points for a homework you need: 1) submit it on time, 2) solve it correctly, or write your own solution, in case you do not know how to solve it (partial results are also counted)
Any kind of cheating constitutes grounds for withholding the course credit.
In case you have any questions regarding material covered during lectures or tutorials, do not hesitate to contact me via email kuznietv@kam.mff.cuni.cz, I am always glad to help you. Just write me your question and we can either make Office Hours or I can answer to you via email.
Tutorial 1 (30 Sep/1 Oct): Generating functions. Exercises