 ČESKÉ VYSOKÉ UČENÍ TECHNICKÉ V PRAZE
STUDIJNÍ PLÁNY
2020/2021

# Linear Algebra

Kód Zakončení Kredity Rozsah Jazyk výuky
BIE-LIN Z,ZK 7 4P+2C anglicky
Přednášející:
Antonella Marchesiello (gar.)
Cvičící:
Jiřina Scholtzová, Antonella Marchesiello (gar.)
Předmět zajišťuje:
katedra aplikované matematiky
Anotace:

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 polynomials 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 error-detecting and error-correcting codes.

Požadavky:

High-school mathematics.

Osnova přednášek:

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 Euclidean algorithm. Binary operation, its properties. Group, ring, field. Homomorphisms (isomorphisms). Properties of a field. Finite fields.

4. Systems 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. Inverse matrices.

9. 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\$.

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

11. Invariant subspaces. Jordan form.

12. 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.

13. Self-correcting codes.

Osnova cvičení:

1. Operations with polynomials.

2. Roots of polynomials. Euclidean algorithm. Greatest common divisor.

3. Sets of linear equations. Gaussian elimination method.

4. Linear dependence and independence.

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

6. Matrices, matrix operations.

7. Determinants and their calculation. Inverse matrices and their calculation.

8. Linear map, linear map matrix.

9. Eigenvalues and eigenvectors of a matrix.

10. Jordan form.

11. Bilinear and quadratic forms.

12. Scalar product, orthogonality. Affine transformation. Translation.

13. Self-correcting codes.

Cíle studia:

The aim of the module is to build the foundations of mathematical way of thinking and provide students with basic knowlege of linear algebra necessary to solve systems of linear equations or problems in 2D and 3D analytic geometry.

Studijní materiály:

1. Pták, P. ''Introduction to Linear Algebra''. ČVUT, Praha, 2005.

Poznámka:

Information about the course and courseware are available at https://courses.fit.cvut.cz/BIE-LIN/

Další informace:
https://courses.fit.cvut.cz/BIE-LIN/
Rozvrh na zimní semestr 2020/2021:
Rozvrh není připraven
Rozvrh na letní semestr 2020/2021:
 06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00 místnost TH:A-1435Marchesiello A.12:45–14:15(přednášková par. 1)Thákurova 7 (FSv-budova A)zasedačka 1435 místnost TH:A-s135Marchesiello A.12:45–14:15(přednášková par. 1)Thákurova 7 (FSv-budova A)As135 místnost TH:A-1447Marchesiello A.09:15–10:45(přednášková par. 1)Thákurova 7 (FSv-budova A)místnost TH:A-942Scholtzová J.11:00–12:30(přednášková par. 1paralelka 101)Thákurova 7 (FSv-budova A) místnost T9:155Marchesiello A.09:15–10:45(přednášková par. 1)DejvicePosluchárnamístnost TH:A-942Scholtzová J.11:00–12:30(přednášková par. 1paralelka 102)Thákurova 7 (FSv-budova A)
Předmět je součástí následujících studijních plánů:
Platnost dat k 18. 4. 2021
Aktualizace výše uvedených informací naleznete na adrese http://bilakniha.cvut.cz/cs/predmet1446506.html