Linear Algebra

Code	Completion	Credits	Range	Language
BI-LIN	Z,ZK	7	4+2	Czech

Lecturer:

Petr Olšák (gar.), Pavel Pták

Tutor:

Petr Olšák (gar.), Lucie Augustovičová, Michal Hroch, Tomáš Kalvoda, Zdeněk Konfršt, Petr Matyáš, Karel Pospíšil, Zdeňka Tischerová

Supervisor:

Department of Applied Mathematics

Synopsis:

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.

Requirements:

Secondary school mathematics.

Syllabus of lectures:

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.

Syllabus of tutorials:

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.

Study Objective:

The goal of the module is to build basic mathematical way of thinking and provide students

Study materials:

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

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

	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
Mon	roomT9:301 Hroch M. 09:15–10:45 (lecture parallel1 parallel nr.101) Dejvice NBFIT učebnaroomT9:301 Hroch M. 11:00–12:30 (lecture parallel1 parallel nr.102) Dejvice NBFIT učebnaroomT9:301 Hroch M. 12:45–14:15 (lecture parallel1 parallel nr.103) Dejvice NBFIT učebnaroomT9:301 Hroch M. 14:30–16:00 (lecture parallel1 parallel nr.104) Dejvice NBFIT učebna roomT9:344 Pospíšil K. 09:15–10:45 (lecture parallel2 parallel nr.201) Dejvice NBFIT ucebnaroomT9:347 Pospíšil K. 11:00–12:30 (lecture parallel2 parallel nr.202) Dejvice NBFIT učebnaroomT9:347 Pospíšil K. 12:45–14:15 (lecture parallel2 parallel nr.203) Dejvice NBFIT učebna roomT9:344 Augustovičová L. 11:00–12:30 (lecture parallel2 parallel nr.213) Dejvice NBFIT ucebna
Tue	roomT9:105 Olšák P. 07:30–09:00 (lecture parallel2) Dejvice PosluchárnaroomT9:301 Olšák P. 11:00–12:30 (lecture parallel2 parallel nr.205) Dejvice NBFIT učebnaroomT9:301 Olšák P. 12:45–14:15 (lecture parallel2 parallel nr.206) Dejvice NBFIT učebnaroomT9:105 Pták P. 14:30–16:00 (lecture parallel1) Dejvice PosluchárnaroomT9:301 Hroch M. 16:15–17:45 (lecture parallel2 parallel nr.208) Dejvice NBFIT učebnaroomT9:301 Hroch M. 18:00–19:30 (lecture parallel1 parallel nr.105) Dejvice NBFIT učebna roomT9:301 Hroch M. 14:30–16:00 (lecture parallel2 parallel nr.207) Dejvice NBFIT učebna
Fri	roomT9:301 Konfršt Z. 07:30–09:00 (lecture parallel1 parallel nr.106) Dejvice NBFIT učebnaroomT9:301 Konfršt Z. 09:15–10:45 (lecture parallel1 parallel nr.107) Dejvice NBFIT učebnaroomT9:301 Konfršt Z. 11:00–12:30 (lecture parallel1 parallel nr.108) Dejvice NBFIT učebnaroomT9:301 Tischerová Z. 12:45–14:15 (lecture parallel2 parallel nr.209) Dejvice NBFIT učebnaroomT9:301 Tischerová Z. 14:30–16:00 (lecture parallel2 parallel nr.210) Dejvice NBFIT učebnaroomT9:301 Tischerová Z. 16:15–17:45 (lecture parallel2 parallel nr.211) Dejvice NBFIT učebna roomT9:105 Pták P. 15:15–17:00 (lecture parallel1) Dejvice Posluchárna
Thu	roomT9:105 Olšák P. 09:15–10:45 (lecture parallel2) Dejvice PosluchárnaroomT9:344 Matyáš P. 12:45–14:15 (lecture parallel2 parallel nr.204) Dejvice NBFIT ucebnaroomT9:301 Pospíšil K. 14:30–16:00 (lecture parallel1 parallel nr.109) Dejvice NBFIT učebnaroomT9:301 Pospíšil K. 16:15–17:45 (lecture parallel1 parallel nr.110) Dejvice NBFIT učebnaroomT9:301 Pospíšil K. 18:00–19:30 (lecture parallel1 parallel nr.111) Dejvice NBFIT učebna
Fri	roomT9:301 Matyáš P. 09:15–10:45 (lecture parallel1 parallel nr.112) Dejvice NBFIT učebnaroomT9:301 Matyáš P. 11:00–12:30 (lecture parallel2 parallel nr.212) Dejvice NBFIT učebnaroomT9:301 Matyáš P. 12:45–14:15 (lecture parallel1 parallel nr.113) Dejvice NBFIT učebna

The course is a part of the following study plans:

Computer Science, Version for Students who Enrolled in 2009 and 2010, Presented in Czech (compulsory course in the program)
Computer engineering, Version for Students who Enrolled in 2009 and 2010, in Czech (compulsory course in the program)
Software Engineering, Version for Students who Enrolled in 2009 and 2010, in Czech (compulsory course in the program)
Web and Multimediac, Version for Students who Enrolled in 2009 and 2010, Presented in Czech (compulsory course in the program)
Information Systems and Management, Version for Students who Enrolled in 2009 and 2010, in Czech (compulsory course in the program)
Information Technology, Version for Students who Enrolled in 2009 and 2010, Presented in Czech (compulsory course in the program)
Informatics, Version for Students who Enrolled in 2009 and 2010, Presented in Czech (compulsory course in the program)
Informatics (Bachelor)- Version for those who Enrolled in 2011 and 2012 (in Czech) (compulsory course in the program)
Information Systems and Management - Version for those who Enrolled in 2011 and 2012 (in Czech) (compulsory course in the program)
Information Technology- Version for those who Enrolled in 2011 and 2012 (in Czech) (compulsory course in the program)
Computer Engineering, Version for those who Enrolled in 2011 and 2012, in Czech (compulsory course in the program)
Software Engineering- Version for those who Enrolled in 2011 and 2012 (in Czech) (compulsory course in the program)
Computer Science - Version for those who Enrolled in 2011 and 2012 (in Czech) (compulsory course in the program)
Web and Multimedia- Version for those who Enrolled in 2011 and 2012 (in Czech) (compulsory course in the program)