Linear Algebra
Code  Completion  Credits  Range  Language 

AE0B01LAG  Z,ZK  7  4+2 
 Lecturer:
 Tutor:
 Supervisor:
 Department of Mathematics
 Synopsis:

This course covers introductory topics of linear algebra. The main focus
is on
the related notions of linear spaces and linear transformations (linear
independence, bases and coordinates) and matrices (determinants, inverse
matrix, matrix of a linear mapping, eigenvalues). Applications include
solving systems of linear equations, geometry in 3space (including dot
product and cross product), and solving linear differential equations.
 Requirements:
 Syllabus of lectures:

1. Introduction, polynomials.
2. Linear spaces, linear dependence and independence.
3. Basis, dimension, coordinates of vectors.
4. Matrices, operations, determinants. Inverse matrix.
5. Systems of linear equations.
6. Linear mappings. Matrix of a linear mapping.
7. Free vectors. Dot product and cross product.
8. Lines and planes in 3dimensional Euclidean space.
9. Eigenvalues and eigenvectors of matrices and linear mappings.
10. Similarity of matrices, matrices similar to diagonal matrices.
11. Generalized eigenvectors.
12. Systems of linear differential equations of 1st order with constant coefficients.
13. Linear differential equations of order n with constant coefficients.
14. Backup class.
 Syllabus of tutorials:

1. Polynomials.
2. Examples of linear spaces, linear independence.
3. Basis, coordinates of vectors.
4. Operations with matrices, determinants. Finding inverse matrix.
5. Systems of linear equations.
6. Examples of linear mappings.
7. Matrix of a linear mapping, change of basis.
8. Dot product and cross product in geometry. Lines and planes.
9. Eigenvalues and eigenvectors of matrices.
10. Diagonalization of matrices.
11. Generalized eigenvectors and applications.
12. Systems of linear differential equations.
13. Linear differential equations of order n.
14. Backup class.
 Study Objective:
 Study materials:

[1] P. Pták: Introduction to Linear Algebra. ČVUT, Praha, 2005.
 Note:
 Further information:
 http://math.feld.cvut.cz/vivi/
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 Cybernetics and Robotics  Robotics (compulsory course in the program)
 Cybernetics and Robotics  Senzors and Instrumention (compulsory course in the program)
 Cybernetics and Robotics  Systems and Control (compulsory course in the program)
 Electrical Engineering, Power Engineering and Management  Applied Electrical Engineering (elective course)
 Electrical Engineering, Power Engineering and Management  Electrical Engineering and Management (elective course)
 Communications, Multimedia and Electronics  Communication Technology (elective course)
 Communications, Multimedia and Electronics  Multimedia Technology (elective course)
 Communications, Multimedia and Electronics  Applied Electronics (elective course)
 Communications, Multimedia and Electronics  Network and Information Technology (elective course)
 Open Informatics  Computer Systems (compulsory course in the program)
 Open Informatics  Computer and Information Science (compulsory course in the program)
 Open Informatics  Software Systems (compulsory course in the program)
 Electrical Engineering, Power Engineering and Management (elective course)
 Communications, Multimedia and Electronics (elective course)
 Cybernetics and Robotics (compulsory course in the program)
 Open Informatics (compulsory course in the program)
 Communications, Multimedia and Electronics  Communications and Electronics (elective course)