Course detail
Linear Algebra I
FSI-SLA Acad. year: 2024/2025 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. Bilinear and quadratic forms.
Supervisor
Department
Learning outcomes of the course unit
Prerequisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Language of instruction
Czech
Aims
Specification of controlled education, way of implementation and compensation for absences
The study programmes with the given course
Programme B-MAI-P: Mathematical Engineering, Bachelor's
branch ---: no specialisation, 6 credits, compulsory
Programme C-AKR-P: , Lifelong learning
branch CZS: , 6 credits, elective
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, operations, inversions.
2. Vector spaces, subspaces, homomorphisms.
3. Linear dependence of vectors, basis and dimension.
4. Transition matrices and linear mapping matrix transformation.
5. Determinants, adjoint matrix.
6. Systems of linear equations.
7. The characteristic polynomial, eigen values, eigen vectors.
8. Jordan normal form.
9. Unitary vector spaces.
10. Orthogonality. Gram-Schmidt process.
11. Bilinear and quadratic forms.
12. Inner, exterior and cross products – relations and applications.
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.