Course detail
Linear Algebra
FSI-SLA Acad. year: 2021/2022 Winter semester
The course deals with following topics: Sets: mappings of sets, relations on a set.
Algebraic operations: groups, vector spaces, matrices and operations on matrices.
Fundamentals of linear algebra: determinants, matrices in step form and rank of a matrix, systems of linear equations. Euclidean spaces: scalar product of vectors, eigenvalues and eigenvectors. Fundamentals of analytic geometry: linear concepts, conics, quadrics.
Language of instruction
Czech
Number of ECTS credits
6
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
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, compulsory
Programme MITAI: Information Technology and Artificial Intelligence, Master's
specialization NADE: Application Development, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
specialization NBIO: Bioinformatics and Biocomputing, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
specialization NCPS: Cyberphysical Systems, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
specialization NEMB: Embedded Systems, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
specialization NGRI: Computer Graphics and Interaction, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
specialization NHPC: High Performance Computing, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
specialization NIDE: Intelligent Devices, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
specialization NISD: Information Systems and Databases, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
specialization NISY: Intelligent Systems, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
specialization NMAL: Machine Learning, compulsory
Programme MITAI: Information Technology and Artificial Intelligence, Master's
specialization NMAT: Mathematical Methods, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
specialization NNET: Computer Networks, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
specialization NSEC: Cybersecurity, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
specialization NSEN: Software Engineering, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
specialization NSPE: Sound, Speech and Natural Language Processing, compulsory
Programme MITAI: Information Technology and Artificial Intelligence, Master's
specialization NVER: Software Verification and Testing, elective
Programme MITAI: Information Technology and Artificial Intelligence, Master's
specialization NVIZ: Computer Vision, elective
Type of course unit
Lecture
39 hours, optionally
Teacher / Lecturer
Syllabus
1. Relations, equivalences, orders, mappings, operations.
2. Number sets, fields.
3. Vector spaces, subspaces, homomorphisms. The linear dependence of vectors, the basis and dimension..
4. Matrices and determinants.
5. Systems of linear equations.
6. The charakteristic polynomial, eigen values, eugen vectors. Jordan normal form.
7. Dual vector spaces. Linear forms.
8. Bilinear and quadratic forms.
9. Schwarz inequality. Orthogonality. Gram-Schmidt process.
10. Inner, exterior, cross and triple products – relations and applications.
11. Affine and euclidean spaces. Geometry of linear objects.
12. Geometry of conics and quadrics.
13. Reserve
Exercise
22 hours, compulsory
Teacher / Lecturer
Syllabus
Week 1: Basics of mathematical logic and operations on sets.
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.