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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 2022
Semester:	winter
E-Credits:	5
Hours per week, examination:	winter s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech, English
Teaching methods:	full-time
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.
Class:	Informatika Bc.
Classification:	Mathematics > Algebra
Is incompatible with:	NUMP003, NALG086

Opinion survey results Examination dates WS schedule Noticeboard

Annotation -

Last update: G_I (11.04.2003)

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

Course completion requirements -

Last update: prof. Mgr. Milan Hladík, Ph.D. (12.09.2022)

To get the tutorial credit, it is necessary to get at least 120 points (out of 240 possible). Points can be obtained throughout the semester from tests and homework assignments. Specification is provided by the particular tutorial teacher.

Those students who get at least 80 points can obtain the required points by solving additional homeworks or passing an additional test (according to the teacher's instructions).

In specific situations (long-term illness, stay abroad, etc.) the tutorial teacher may set individual conditions for obtaining the credit.

Obtaining the tutorial credit is a necessary condition for taking the exam.

Literature -

Last update: Andrew Goodall, D.Phil. (11.10.2017)

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

Teaching methods -

Last update: prof. Mgr. Milan Hladík, Ph.D. (29.09.2020)

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

Requirements to the exam -

Last update: doc. Mgr. Jan Hubička, Ph.D. (13.06.2022)

The exam is primarily oral. The students will be given enough time to prepare their answers in written form.

The exam is focused on theory - knowledge of concepts, facts, arguments and applications (i.e. definitions, theorems, proofs and examples).

Result of tests accomplished during the teaching period may be taken into account at the exam.

Class credits ("zápočet") are prerequisite for taking the examination.

Syllabus -

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

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