Course detail
Linear Algebra I
FSI-SLA Acad. year: 2023/2024 Winter semester
The course deals with the following topics: Vector spaces, matrices and operations on matrices. Consequently, determinants, matrices in a step form and the rank of a matrix, systems of linear equations. Euclidean spaces: scalar product of vectors, eigenvalues and eigenvectors, Jordan canonical form. Fundamentals of analytic geometry, linear objects.
Supervisor
Department
Learning outcomes of the course unit
Students will be made familiar with algebraic operations,linear algebra, vector and Euclidean spaces, and analytic geometry. They will be able to work with matrix operations, solve systems of linear equations and apply the methods of linear algebra to analytic geometry and engineering tasks. When completing the course, the students will be prepared for further study of mathematical and technical disciplines.
Prerequisites
Students are expected to have basic knowledge of secondary school mathematics.
Planned learning activities and teaching methods
The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.
Assesment methods and criteria linked to learning outcomes
Course-unit credit requirements: Active attendance at the seminars, at least 50% of points in written tests. There is one alternative date to correct these tests.
Form of examinations: The exam is written and has two parts.
The exercises part takes 100 minutes and 6 exercises are given to solve.
The theoretical part takes 20 minutes and 6 questions are asked.
At least 50% of the correct results must be obtained from each part. If less is met in one of the parts, then the classification is F (failed).
Exercises are evaluated by 3 points, questions by 1 point.
If 50% of each part is met, the total classification is given by the sum.
A (excellent): 22 – 24 points
B (very good): 20 – 21 points
C (good): 17 – 19 points
D (satisfactory): 15 – 16 points
E (enough): 12 – 14 points
F (failed): 0 – 11 points
Language of instruction
Czech
Aims
The course aims to acquaint the students with the basics of algebraic operations, linear algebra, vector and Euclidean spaces, and analytic geometry. This will enable them to attend further mathematical and engineering courses and deal with engineering problems. Another goal of the course is to develop the students' logical
thinking.
Specification of controlled education, way of implementation and compensation for absences
Attendance at lectures is recommended, attendance at seminars is required. The lessons are planned on the basis of a weekly schedule. The way of compensation for an absence is in the competence of the teacher.
The study programmes with the given course
Programme B-MAI-P: Mathematical Engineering, Bachelor's
branch ---: no specialisation, 6 credits, compulsory
Programme MITAI: Information Technology and Artificial Intelligence, Master's
branch NADE: Application Development, 6 credits, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
branch NBIO: Bioinformatics and Biocomputing, 6 credits, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
branch NCPS: Cyberphysical Systems, 6 credits, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
branch NEMB: Embedded Systems, 6 credits, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
branch NGRI: Computer Graphics and Interaction, 6 credits, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
branch NHPC: High Performance Computing, 6 credits, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
branch NIDE: Intelligent Devices, 6 credits, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
branch NISD: Information Systems and Databases, 6 credits, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
branch NISY: Intelligent Systems, 6 credits, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
branch NMAL: Machine Learning, 6 credits, compulsory
Programme MITAI: Information Technology and Artificial Intelligence, Master's
branch NMAT: Mathematical Methods, 6 credits, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
branch NNET: Computer Networks, 6 credits, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
branch NSEC: Cybersecurity, 6 credits, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
branch NSEN: Software Engineering, 6 credits, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
branch NSPE: Sound, Speech and Natural Language Processing, 6 credits, compulsory
Programme MITAI: Information Technology and Artificial Intelligence, Master's
branch NVER: Software Verification and Testing, 6 credits, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
branch NVIZ: Computer Vision, 6 credits, elective
Type of course unit
Lecture
39 hours, optionally
Teacher / Lecturer
Syllabus
1. Number sets, fields. Vector spaces, subspaces, homomorphisms.
2. Linear dependence of vectors, basis and dimension.
3. Matrices and determinants.
4. Systems of linear equations.
5. The characteristic polynomial, eigen values, eigen vectors.
6. Jordan normal form.
7. Euclidean and unitary vector spaces.
8. Dual vector spaces. Linear forms.
9. Bilinear and quadratic forms.
10. Orthogonality. Gram-Schmidt process.
11. Inner, exterior and cross products – relations and applications.
12. Affine and euclidean spaces. Geometry of linear objects.
13. Reserve
Exercise
22 hours, compulsory
Teacher / Lecturer
Syllabus
Week 1: Fundamental notions such as vectors, matrices and operations.
Following weeks: Seminar related to the topic of the lecture given in the previous week.
Computer-assisted exercise
4 hours, compulsory
Syllabus
Seminars with computer support are organized according to current needs. They enables students to solve algorithmizable problems by computer algebra systems.