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A course is the basic teaching unit, it's design as a medium for a student to acquire comprehensive knowledge and skills indispensable in the given field. A course guarantor is responsible for the factual content of the course.
For each course, there is a department responsible for the course organisation. A person responsible for timetabling for a given department sets a time schedule of teaching and for each class, s/he assigns an instructor and/or an examiner.
Expected time consumption of the course is expressed by a course attribute extent of teaching. For example, extent = 2 +2 indicates two teaching hours of lectures and two teaching hours of seminar (lab) per week.
At the end of each semester, the course instructor has to evaluate the extent to which a student has acquired the expected knowledge and skills. The type of this evaluation is indicated by the attribute completion. So, a course can be completed by just an assessment ('pouze zápočet'), by a graded assessment ('klasifikovaný zápočet'), or by just an examination ('pouze zkouška') or by an assessment and examination ('zápočet a zkouška') .
The difficulty of a given course is evaluated by the amount of ECTS credits.
The course is in session (cf. teaching is going on) during a semester. Each course is offered either in the winter ('zimní') or summer ('letní') semester of an academic year. Exceptionally, a course might be offered in both semesters.
The subject matter of a course is described in various texts.

BIE-LA1.21 Linear Algebra 1 Extent of teaching: 2P+1R+1C
Instructor: Forough M. Completion: Z,ZK
Department: 18105 Credits: 5 Semester: Z

Annotation:
We will introduce students to the basic concepts of linear algebra, such as vectors, matrices, vector spaces. We will define vector spaces over the field of real and complex numbers and also over finite fields. We will present the concepts of basis and dimension and learn to solve systems of linear equations using the Gaussian elimination method (GEM) and show the connection with linear manifolds. We define the regularity of matrices and learn to find their inversions using GEM. We will also learn to find eigenvalues and eigenvectors of a matrix. We will also demonstrate some applications of these concepts in computer science.

Lecture syllabus:
1. Fields, vectors, and vector spaces.
2. Matrices, matrix operations and matrix notation of a system of linear equations.
3. Solving systems of linear equations using Gauss elimination method.
4. Linear (in)dependence of vectors, linear span, subspace.
5. Base, dimension of a vector (sub)space.
6. Matrix rank, regularity of a matrix, inverse of matrix and its computation.
7. Frobenius theorem on solutions of a system of linear equations.
9. Linear manifolds, parametric and non-parametric equations of linear manifolds.
10. Permutations, determinant of a matrix.
11. [2] Eigenvalues and eigenvectors of matrices.
13. Diagonalization of matrices.

Seminar syllabus:
1. Matrices, matrix operations. Solving systems of linear equations using Gauss elimination method.
2. Linear (in)dependence of vectors, linear span, subspace. Base, dimension of a vector (sub)space.
3. Matrix rank, regularity of a matrix, inverse of matrix and its computation.
4. Frobenius theorem on solutions of a system of linear equations.
5. Linear manifolds, parametric and non-parametric equations of linear manifolds. Determinant of a matrix.
6. Eigenvalues and eigenvectors of matrices. Diagonalization of matrices.

Literature:
1 Strang G. : Introduction to Linear Algebra (5th Edition). Wellesley-Cambridge Press, 2016. ISBN 978-0980232776.
2. Lay D.C., Lay S.R., McDonald J.J. : Linear Algebra and Its Applications (5th Edition). Pearson, 2015. ISBN 978-0321982384.
3. Axler S. : Linear Algebra Done Right (3rd Edition). Springer, 2014. ISBN 978-3319110790.
4. Klein P. N. : Coding the Matrix: Linear Algebra through Applications to Computer Science. Newtonian Press, 2013. ISBN 978-0615880990.

Requirements:
The ability to think mathematically and knowledge of a high school mathematics.

Chybí některá textová pole,vyplněny mají být anotace, požadavky, osnova (sylabus), osnova cvičení, studijní materiály, klíčová slova, CZ i EN, webová strana předmětu

The course is also part of the following Study plans:
Study Plan Study Branch/Specialization Role Recommended semester
BIE-PI.21 Computer Engineering 2021 PP 1
BIE-PV.21 Computer Systems and Virtualization 2021 PP 1
BIE-PS.21 Computer Networks and Internet 2021 PP 1
BIE-TI.21 Computer Science 2021 PP 1
BIE-SI.21 Software Engineering 2021 PP 1
BIE-IB.21 Information Security 2021 (Bachelor in English) PP 1


Page updated 29. 3. 2024, semester: L/2021-2, Z,L/2023-4, Z/2021-2, Z/2020-1, Z/2019-20, L/2020-1, Z,L/2022-3, L/2019-20, Send comments to the content presented here to Administrator of study plans Design and implementation: J. Novák, I. Halaška