Linear Algebra and its Applications
Code  Completion  Credits  Range  Language 

AE0B01LAA  Z,ZK  8  3+3 
 Lecturer:
 Tutor:
 Supervisor:
 Department of Mathematics
 Synopsis:

The course covers standard basics of matrix calculus (determinants, inverse matrix) and linear algebra (linear space,basis, dimension, euclidean spaces, linear transformations) including eigenvalues and eigenvectors. Notions are illustrated in applications: matrices are used when solving systems of linear equations, eigenvalues are used for solving systems of linear differential equations.
 Requirements:

In order to obtain the certificate of attendance,
students are required to actively participate in the laboratory class, hand in the assigned
homework and obtain a sufficient score during lab tests. Only students who obtain attendance certificate („zapocet“) are allowed to take the exam.
 Syllabus of lectures:

1.Systems of linear equations. Gauss elimination method.
2. Linear spaces, linear dependence and independence.
3. Basis, dimension, coordinates of vectors.
4. Rank of a matrix, the Frobenius theorem.
5. Linear mappings. Matrix of a linear mapping.
6. Matrix multiplication, inverse matrix. Determinants.
7.Inner product.Expanding vector w.r.t. orthonormal basis. Fourier basis.
8. Eigenvalues and eigenvectors of matrices and linear mappings.
9. Differential equations. Method of separation of variables.
10. Linear differential equations, homogeneous and nonhomogeneous. Variation of parameter.
11.Linear differential equations with constant coefficients. Basis of solutions. Solving
nonhomogeneous differential equations.
12.Systems of linear differential equations with constant coefficients. Basis of solutions.Solving nonhomogeneous systems.
13.Applications. Numerical aspects.
 Syllabus of tutorials:

1.Systems of linear equations. Gauss elimination method.
2. Linear spaces, linear dependence and independence.
3. Basis, dimension, coordinates of vectors.
4. Rank of a matrix, the Frobenius theorem.
5. Linear mappings. Matrix of a linear mapping.
6. Matrix multiplication, inverse matrix. Determinants.
7.Inner product.Expanding vector w.r.t. orthonormal basis. Fourier basis.
8. Eigenvalues and eigenvectors of matrices and linear mappings.
9. Differential equations. Method of separation of variables.
10. Linear differential equations, homogeneous and nonhomogeneous. Variation of parameter.
11.Linear differential equations with constant coefficients. Basis of solutions. Solving
nonhomogeneous differential equations.
12.Systems of linear differential equations with constant coefficients. Basis of solutions.Solving nonhomogeneous systems.
13.Applications. Numerical aspects.
 Study Objective:
 Study materials:

1. P. Pták: Introduction to Linear Algebra. ČVUT, Praha, 2005.
2. P. Pták: Introduction to Linear Algebra. ČVUT, Praha, 1997. ftp://math.feld.cvut.cz/pub/krajnik/vyuka/ua/linalgeb.pdf
 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 (elective course)
 Cybernetics and Robotics  Senzors and Instrumention (elective course)
 Cybernetics and Robotics  Systems and Control (elective course)
 Electrical Engineering, Power Engineering and Management  Applied Electrical Engineering (compulsory course in the program)
 Electrical Engineering, Power Engineering and Management  Electrical Engineering and Management (compulsory course in the program)
 Communications, Multimedia and Electronics  Communication Technology (compulsory course in the program)
 Communications, Multimedia and Electronics  Multimedia Technology (compulsory course in the program)
 Communications, Multimedia and Electronics  Applied Electronics (compulsory course in the program)
 Communications, Multimedia and Electronics  Network and Information Technology (compulsory course in the program)
 Open Informatics  Computer Systems (elective course)
 Open Informatics  Computer and Information Science (elective course)
 Open Informatics  Software Systems (elective course)
 Electrical Engineering, Power Engineering and Management (compulsory course in the program)
 Communications, Multimedia and Electronics (compulsory course in the program)
 Cybernetics and Robotics (elective course)
 Open Informatics (elective course)
 Communications, Multimedia and Electronics  Communications and Electronics (compulsory course in the program)