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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.

BI-LIN Linear Algebra Extent of teaching: 4P+2C
Instructor: Dombek D. Completion: Z,ZK
Department: 18105 Credits: 7 Semester: L

Annotation:
The course is taught in Czech. Students understand the theoretical foundation of algebra and mathematical principles of linear models of systems around us, where the dependencies among components are only linear. They know the basic methods for operating with matrices and linear spaces. They are able to perform matrix operations and solve systems of linear equations. They can apply these mathematical principles to solving problems in 2D or 3D analytic geometry. They understand the error-detecting and error-correcting codes.

Lecture syllabus:
Course lectures is taught in Czech.
1. Polynomials, roots of polynomials, irreducible polynomials. Polynomials in R, C, Q.
2. Sets of linear equations. Gaussian elimination method.
3. Linear spaces, axiomatic definition.
4. Linear combination and linear independence.
5. Bases, dimensions, vector coordinates in a base.
6. Linear maps (homomorphism, isomorphism), kernel, defect, composition of maps.
7. Matrices, matrix operations.
8. Determinants.
9. Inverse matrix, its calculation.
10. Matrix of homomorphism. Rotation, projection onto a straight line (plane), symmetry with respect to a straight line (plane) in R^2, R^3. Transformation of coordinates.
11. Eigenvalues and eigenvectors of a matrix or a linear map.
12. Scalar product, orthogonality. Euclidean and unitary space. Linear map of Euclidean and unitary spaces. Affine space. Affine transformation. Translation.
13. Group, ring, field. Properties of a field. Finite fields.
14. Self-correcting codes.

Seminar syllabus:
The course seminary is taught in Czech. Students understand the theoretical foundation of algebra and mathematical principles of linear models of systems around us, where the dependencies among components are only linear. They know the basic methods for operating with matrices and linear spaces. They are able to perform matrix operations and solve systems of linear equations. They can apply these mathematical principles to solving problems in 2D or 3D analytic geometry. They understand the error-detecting and error-correcting codes.
1. Operations with polynomials. Roots of polynomials.
2. Sets of linear equations. Gaussian elimination method.
3. Linear dependence and independence.
4. Bases, dimensions, vector coordinates in a base. Coordinate transformations.
5. Matrices, matrix operations.
6. Determinants and their calculation.
7. Inverse matrix and its calculation.
8. Sets of linear equations. Cramer's Theorem.
9. Linear map, linear map matrix.
10. Eigenvalues and eigenvectors of a matrix.
11. Scalar product, orthogonality.
12. Affine transformation. Translation.
13. Group, ring, field. Properties of a field. Finite fields.
14. Self-correcting codes.

Literature:
The course is taught in Czech.
1. Pták, P. Introduction to Linear Algebra. ČVUT, Praha, 2005.

Requirements:
Secondary school mathematics.

Informace o předmětu a výukové materiály naleznete na https://courses.fit.cvut.cz/BI-LIN/
Chybí klíčová slova.

The course is also part of the following Study plans:
Study Plan Study Branch/Specialization Role Recommended semester
BI-SPOL.2015 Unspecified Branch/Specialisation of Study PP 2
BI-WSI-PG.2015 Web and Software Engineering PP 2
BI-WSI-WI.2015 Web and Software Engineering PP 2
BI-WSI-SI.2015 Web and Software Engineering PP 2
BI-ISM.2015 Information Systems and Management PP 2
BI-ZI.2018 Knowledge Engineering PP 2
BI-PI.2015 Computer engineering PP 2
BI-TI.2015 Computer Science PP 2
BI-BIT.2015 Computer Security and Information technology PP 2


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