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Course, academic year 2023/2024
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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
4EU+: no
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
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 2023 (English section) are specified on the course web page:

https://iuuk.mff.cuni.cz/~ipenev/NMAI057W2023.html

Last update: Penev Irena, Ph.D. (13.10.2023)
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 2023 can be found on the course web page: https://iuuk.mff.cuni.cz/~ipenev/NMAI057W2023.html

Last update: Penev Irena, Ph.D. (13.10.2023)
Teaching methods -

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

Course web page for Winter 2023: https://iuuk.mff.cuni.cz/~ipenev/NMAI057W2023.html

Last update: Penev Irena, Ph.D. (13.10.2023)
Requirements to the exam -

In Winter 2023 (English section), the exam will be written. Tutorial credit ("zápočet") is a prerequisite for taking the exam.

Last update: Penev Irena, Ph.D. (13.10.2023)
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)
 
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