SubjectsSubjects(version: 941)
Course, academic year 2023/2024
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Linear algebra - OKB2310N09
Title: Lineární algebra
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2022
Semester: summer
E-Credits: 4
Examination process: summer s.:combined
Hours per week, examination: summer s.:0/0, C+Ex [HS]
Extent per academic year: 15 [hours]
Capacity: unknown / unknown (200)
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: not taught
Language: Czech
Teaching methods: combined
Teaching methods: combined
Note: course can be enrolled in outside the study plan
enabled for web enrollment
priority enrollment if the course is part of the study plan
Guarantor: prof. RNDr. Jarmila Novotná, CSc.
doc. RNDr. Antonín Jančařík, Ph.D.
Class: Matematika 1. cyklus - povinné
Classification: Mathematics > Mathematics General
Pre-requisite : OKB2310008
Interchangeability : OB2310N009, OKB2310009
Is pre-requisite for: OKB2310260, OKB1310506, OKB1310N11, OKB1310N03, OKB2310N10
Is interchangeable with: OKB2310208
Annotation -
Last update: JANCARIK/PEDF.CUNI.CZ (09.08.2012)
The basic course focusing on vector spaces, matrices, systems of linear equations, determinants and linear mappings. The gained knowledge and skills belong to the basic elements necessary for further mathematics courses.
Aim of the course -
Last update: JANCARIK/PEDF.CUNI.CZ (09.08.2012)

Subject aiming to acquaint students with these basic parts of algebra and theoretical arithmetic on which school mathematics is based and which serve as tools for other mathematical disciplines in teacher training.

Literature -
Last update: JANCARIK/PEDF.CUNI.CZ (09.08.2012)

BLAŽEK, J. a kol.: Algebra a teoretická aritmetika 1. Praha: SPN, 1983.

KATRIŇÁK, T. a kol.: Algebra a teoretická aritmetika 1. Bratislava, Praha: ALFA, SNTL, 1985.

NOVOTNÁ, J. ? TRCH, M.: Algebra a teoretická aritmetika, Sbírka příkladů část 1, Lineární algebra. 2. vyd. Praha: Karolinum, 2005. Praha: Karolinum, 1995.

DEMLOVÁ, M. ? NAGY, J.: Algebra. Praha: SNTL, 1985.

Teaching methods -
Last update: JANCARIK/PEDF.CUNI.CZ (09.08.2012)

Lecture & practice, in some cases supported by e-learning materials (determinants).

Requirements to the exam - Czech
Last update: PhDr. Jiří Bureš, Ph.D. (24.02.2015)

Požadavky k zápočtu:
Úspěšné vypracování zápočtové písemné práce

Požadavky ke zkoušce:
Písemná a ústní zkouška
1) úspěšné zvládnutí počítání s vektory, maticemi a determinanty, studium vlastností vektorových prostorů a lineárních zobrazení
2) úspěšné zvládnutí základních teoretických pojmů a jejich vzájemných souvislostí (včetně důkazů)

Syllabus -
Last update: JANCARIK/PEDF.CUNI.CZ (09.08.2012)
  • Vector spaces over the field and their subspaces. Intersections and linear, resp. direct sums. Linear combination of vectors, spanning sets, linear dependence and independence. Steinitz theorem, basis and dimension of a vector space.
  • Matrix over a field, type and rank of a matrix. Operations with matrices, transposed, inverse, regular and singular matrices.
  • Systems of linear equations over a field, homogeneous and nonhomogeneous, solvability.
  • Permutations. Determinant of a matrix. Cofactors and adjoints. Laplace expansion. Determinants and matrix inverses. Cramer rule.
  • Linear mapping, composed and inverse mapping.Lineární zobrazení.
  • Scalar and vector products.

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