Subjects

Your browser does not support JavaScript, or its support is disabled. Some features may not be available.

Linear Algebra 1 - NMAI057

Title:	Lineární algebra 1
Guaranteed by:	Department of Applied Mathematics (32-KAM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2025
Semester:	winter
E-Credits:	5
Hours per week, examination:	winter s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech, English
Teaching methods:	full-time
Additional information:	https://kam.mff.cuni.cz/~hladik/LA

Guarantor:	prof. Mgr. Milan Hladík, Ph.D. doc. Mgr. Petr Kolman, Ph.D.
Teacher(s):	Mgr. Todor Antić Bc. Jakub Černý RNDr. Martin Černý prof. RNDr. Jiří Fiala, Ph.D. Mgr. Elif Garajová, Ph.D. Bc. Vladimír Chudý doc. Mgr. Petr Kolman, Ph.D. Mgr. Martin Koreček RNDr. Matyáš Lorenc RNDr. Jana Maxová, Ph.D. Mgr. Adam Morawski RNDr. Ondřej Pangrác, Ph.D. Irena Penev, Ph.D. Amit Roy, M.Sc. Mgr. Sasha Sami Mgr. Matej Straka
Class:	Informatika Bc.
Classification:	Mathematics > Algebra
Is incompatible with:	NUMP003, NALG086

Opinion survey results WS schedule Noticeboard

Annotation -

Basics of linear algebra (vector spaces and linear maps, solutions of linear equations, matrices).

Last update: G_I (11.04.2003)

Course completion requirements -

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.

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.

Last update: Maxová Jana, RNDr., Ph.D. (01.10.2025)

Literature -

D. Poole. Linear Algebra, A Modern Introduction. 3rd Int. Ed., Brooks Cole, 2011. Chapters 1,2,3,6.

Also useful:

G. Strang. Linear algebra and its applications. Thomson, USA, 4rd edition, 2006.

C. D. Meyer. Matrix analysis and applied linear algebra. SIAM, Philadelphia, PA, 2000.

W. Gareth. Linear Algebra with Applications. Jones and Bartlett Publishers, Boston, 4th edition, 2001.

R. Beezer, A First Course in Linear Algebra - a free online textbook. http://linear.ups.edu/html/fcla.html

Lecture Notes for Winter 2024: https://iuuk.mff.cuni.cz/~ipenev/LALectureNotes.pdf

Last update: Penev Irena, Ph.D. (02.10.2024)

Teaching methods -

Additional information can be found on the instructor's website https://kam.mff.cuni.cz/~kolman/vyuka.html

Last update: Maxová Jana, RNDr., Ph.D. (25.09.2025)

Requirements to the exam -

The exam requirements correspond to the syllabus of the course in the scope covered during lectures, exercises, and assigned self-study. The ability to apply the acquired knowledge when solving problems is also required.

The exam typically consists of a written and an oral part.

The course credit ("zápočet") is a prerequisite for taking the exam.

The results of tests taken during the course may be considered during the exam.

Last update: Maxová Jana, RNDr., Ph.D. (25.09.2025)

Syllabus -

Systems of linear equations:

matrix form, elementary row operations, row echelon form

Gaussian elimination

Gauss-Jordan elimination

Matrices:

matrix operations, basic types of matrices

nonsingular matrix, inverse of a matrix

Algebraic structures:

groups, subgroups, permutations

fields and finite fields in particular

Vector spaces:

linear span, linear combination, linear dependence and independence

basis and its existence, coordinates

Steinitz' replacement theorem

dimension, dimensions of sum and intersection of subspaces

fundamental matrix subspaces (row space, column space, kernel)

rank-nullity theorem

Linear maps:

examples, image, kernel

injective linear maps

matrix representations, transition matrix, composition of linear maps

isomorphism of vector spaces

Topics on expansion:

introduction to affine spaces and relation to linear equations

LU decomposition

Last update: Hladík Milan, prof. Mgr., Ph.D. (11.05.2020)