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Linear Algebra 1 - NMAI057

Title:	Lineární algebra 1
Guaranteed by:	Department of Applied Mathematics (32-KAM)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2024
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):	RNDr. Martin Černý doc. RNDr. Jiří Fiala, Ph.D. Mgr. Elif Garajová, Ph.D. prof. Mgr. Milan Hladík, Ph.D. Bc. Vladimír Chudý doc. Mgr. Petr Kolman, Ph.D. Mgr. Matyáš Lorenc RNDr. Jana Maxová, Ph.D. RNDr. Ondřej Pangrác, Ph.D. Irena Penev, Ph.D.
Class:	Informatika Bc.
Classification:	Mathematics > Algebra
Is incompatible with:	NUMP003, NALG086

Opinion survey results Examination dates 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 -

Tutorial credit ("zápočet") is a prerequisite for taking the exam. Tutorial requirements for Winter 2024 (English section) are specified on the course web page:

https://iuuk.mff.cuni.cz/~ipenev/NMAI057W2024.html

Last update: Penev Irena, Ph.D. (12.10.2024)

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 -

Moodle course: https://dl1.cuni.cz/course/view.php?id=10373&lang=en

Course web page for Winter 2024: https://iuuk.mff.cuni.cz/~ipenev/NMAI057W2024.html

Last update: Penev Irena, Ph.D. (12.10.2024)

Requirements to the exam -

In Winter 2024 (English section), the exam will be written. In rare cases, a student may be invited to take an oral exam (in addition to the written exam). Tutorial credit ("zápočet") is a prerequisite for taking the exam.

Last update: Penev Irena, Ph.D. (12.10.2024)

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)