M2110B Linear Algebra and Geometry II

Faculty of Science
Spring 2026
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
In-person direct teaching
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
prof. RNDr. Jan Paseka, CSc. (seminar tutor)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 16. 2. to Fri 22. 5. Tue 10:00–11:50 A,01026
  • Timetable of Seminar Groups:
M2110B/01: Mon 16. 2. to Fri 22. 5. Thu 10:00–11:50 M1,01017, M. Čadek
M2110B/02: Mon 16. 2. to Fri 22. 5. Mon 14:00–15:50 M2,01021, J. Paseka
Prerequisites
M1110B Linear Algebra I
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Abstract
The aim of this second course in linear algebra is to introduce other basic notions of linear algebra. Passing the course the students *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Learning outcomes
Passing the course the students *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Key topics
Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Linear models. Markov processes. Lislie population model. Ortogonal and unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations. Singular value decomposion. QR decomposition.
Study resources and literature
  • PAVOL, Zlatoš. Lineárna algebra a geometria (Linear algebra and geometry). Bratislava: Albert Marenčin PT, s.r.o., 2011, 741 pp. ISBN 978-80-8114-111-9. info
  • PASEKA, Jan and Pavol ZLATOŠ. Lineární algebra a geometrie I. Elportál. Brno: Masarykova univerzita, 2010. ISSN 1802-128X. URL info
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Approaches, practices, and methods used in teaching
Lectures and exercises (tutorials).
Method of verifying learning outcomes and course completion requirements
The exam consists of three parts: 1. Semester-long component: You need to score at least 50% of the points in 6 short written tests. 2. Written exam during the exam period: The written exam consists of a numerical and a theoretical part. You need to score a total of 12 points out of 22. 3. Oral exam: Students who pass both parts of the written exam proceed to the oral exam. During the oral exam, you will be required to demonstrate understanding of the topics covered and the ability to illustrate the concepts and theorems with examples. Exam requirements: Mastery of the material covered in lectures and tutorials. In the case of distance learning, the material is available on the course website throughout the semester. You will be asked about definitions, theorems, examples, and proofs. Emphasis is placed on understanding. It is not enough to know the definitions and theorems; you need to be able to provide examples of the defined concepts and the main theorems. You are also required to be able to perform simple proofs. Additional notes: The instructor is happy to answer your questions during lectures and tutorials if you do not understand something. There are many resources available to help you prepare for the exam, including the textbook, lecture notes, and online materials.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
Information on completion of the course: ukončení zápočtem možné pouze rozhodnutím učitele
The course is taught annually.
Credit evaluation note: 2 kr. zápočet.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~cadek
The course is also listed under the following terms Spring 2025, Spring 2027.
  • Enrolment Statistics (recent)
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