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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.

BIK-LIN Linear Algebra Extent of teaching: 26KP+4KC

Instructor: Klouda K. Completion: Z,ZK

Department: 18105 Credits: 7 Semester: L

Annotation:
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:

1. Introduction: definition, theorem, proof. Types of proofs.

2. Set operations: Intersection, union, relative complement, Cartesian product. Maps, composite maps, inverse map, bijection, permutation.

3. Polynomials, roots of polynomials, irreducible polynomials. Polynomials in R, C, Q. Greatest common divisor and Euclid's algorithm. Binary operation, its properties. Group, ring, field. Homomorphisms (isomorphisms). Properties of a field. Finite fields.

4. Sets of linear equations. Gaussian elimination method.

5. Linear spaces, linear combination and linear independence.

6. Bases, dimensions, vector coordinates in a base. Coordinate transformations.

7. Matrices, matrix operations.

8. Determinants.

9. Inverse matrix, its calculation.

10. Linear map, linear map matrix. Rotation, projection onto a straight line (plane), symmetry with respect to a straight line (plane) in $R^2$, $R^3$.

11. Eigenvalues and eigenvectors of a matrix or a linear map.

12. Invariant subspaces. Jordan form.

13. Bilinear and quadratic forms. Scalar product, orthogonality. Orthogonal complement. Euclidean and unitary space. Linear map of Euclidean and unitary spaces. Affine space. Affine transformation. Translation.

14. Self-correcting codes.

Seminar syllabus:

1. Operations with polynomials. Roots of polynomials. Euclid's algorithm. Greatest common divisor. Sets of linear equations. Gaussian elimination method. Linear dependence and independence. Bases, dimensions, vector coordinates in a base. Coordinate transformations. Matrices, matrix operations. Determinants and their calculation.

2. Inverse matrix and its calculation. Linear map, linear map matrix. Eigenvalues and eigenvectors of a matrix. Jordan form. Bilinear and quadratic forms. Scalar product, orthogonality. Affine transformation. Translation. Self-correcting codes.

Literature:

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/

The course is also part of the following Study plans:

Study Plan Study Branch/Specialization Role Recommended semester

BIK-SPOL.2015 Unspecified Branch/Specialisation of Study PP 2

BIK-BIT.2020 Computer Security and Information technology PP 2

BIK-WSI-SI.2015 Web and Software Engineering PP 2

BIK-BIT.2015 Computer Security and Information technology PP 2

Page updated 19. 4. 2024, semester: L/2020-1, L/2021-2, Z/2023-4, Z/2024-5, Z/2019-20, Z/2022-3, L/2019-20, L/2022-3, Z/2020-1, Z/2021-2, L/2023-4, Send comments to the content presented here to Administrator of study plans Design and implementation: J. Novák, I. Halaška

BIK-LIN	Linear Algebra			Extent of teaching:	26KP+4KC
Instructor:	Klouda K.			Completion:	Z,ZK
Department:	18105	Credits:	7	Semester:	L

1.		Introduction: definition, theorem, proof. Types of proofs.
2.		Set operations: Intersection, union, relative complement, Cartesian product. Maps, composite maps, inverse map, bijection, permutation.
3.		Polynomials, roots of polynomials, irreducible polynomials. Polynomials in R, C, Q. Greatest common divisor and Euclid's algorithm. Binary operation, its properties. Group, ring, field. Homomorphisms (isomorphisms). Properties of a field. Finite fields.
4.		Sets of linear equations. Gaussian elimination method.
5.		Linear spaces, linear combination and linear independence.
6.		Bases, dimensions, vector coordinates in a base. Coordinate transformations.
7.		Matrices, matrix operations.
8.		Determinants.
9.		Inverse matrix, its calculation.
10.		Linear map, linear map matrix. Rotation, projection onto a straight line (plane), symmetry with respect to a straight line (plane) in $R^2$, $R^3$.
11.		Eigenvalues and eigenvectors of a matrix or a linear map.
12.		Invariant subspaces. Jordan form.
13.		Bilinear and quadratic forms. Scalar product, orthogonality. Orthogonal complement. Euclidean and unitary space. Linear map of Euclidean and unitary spaces. Affine space. Affine transformation. Translation.
14.		Self-correcting codes.

1.		Operations with polynomials. Roots of polynomials. Euclid's algorithm. Greatest common divisor. Sets of linear equations. Gaussian elimination method. Linear dependence and independence. Bases, dimensions, vector coordinates in a base. Coordinate transformations. Matrices, matrix operations. Determinants and their calculation.
2.		Inverse matrix and its calculation. Linear map, linear map matrix. Eigenvalues and eigenvectors of a matrix. Jordan form. Bilinear and quadratic forms. Scalar product, orthogonality. Affine transformation. Translation. Self-correcting codes.