Czech

Not applicable.

The work during the semester is assessed with a maximum of 30 points (these points can be obtained for tests, homework). In addition, a maximum of 10 bonus points can be earned for bonus homework, additional theoretical questions and increased activity in practical exercises. Students must earn at least 10 points to receive credit. The final written examination is marked with a maximum of 70 points. It consists of examples verifying the mastery of algorithms and theoretical questions (total of 5 points in matrix calculus and 5 points in numerical methods). To pass the exam, the student must obtain at least 10 points in the matrix calculations section and at least 10 points in the numerical methods section. The definition of supervised learning and the way it is carried out are given in the annually updated regulation of the course guarantor.

The aim of this course is to introduce the basics of vector and matrix calculus in real and complex domain and basic numerical solution methods of systems of equations.
Students completing this course should be able to:
- decide whether vectors are linearly independent and whether they form a basis of a vector space (in the real and complex field)
- add and multiply matrices, compute the determinant of a square matrix to the 4x4 type, compute the rank and the inverse of a matrix
- solve a system of linear equations
- compute eigenvalues and eigenvectors of a matrix
- analyze the definiteness of a matrix also using eigenvalues
- compute a matrix exponential for certain classes of matrices
- solve matrices systems of linear equations
- find the root of a given equation f(x)=0 using the bisection method, Newton method or the iterative method, describe these methods including the convergence conditions
- solve a system of linear equations using Gaussian elimination with pivoting, Jacobi and Gauss-Seidel iteration methods, discuss the advantages and disadvantages of these methods
- find the approximation of a function by spline functions
- find the approximation of a function given by table of points by the least squares method (linear, quadratic or exponential approximation)
- estimate the derivative of a given function using numerical differentiation
- compute the numerical approximation of a definite integral using trapezoidal and Simpson method, describe the principal of these methods, compare them according to their accuracy

Not applicable.

Not applicable.

M. Dont: Maticová analýza, skripta, nakl. ČVUT 2011 (CS)
FAJMON, B., HLAVIČKOVÁ, I., NOVÁK, M., Matematika 3. Elektronický text FEKT VUT, Brno, 2013 (CS)
SCHMIDTMAYER, J., Maticový počet a jeho použití v technice, SNTL Praha 1974 (CS)

HRUZA, B., MRHAČOVÁ, H., Cvičení z algebry a geometrie. Ediční stř. VUT 1993, skriptum. (CS)