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Course detail
FSI-SLAAcad. year: 2023/2024
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.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Entry knowledge
Rules for evaluation and completion of the course
Aims
Study aids
Prerequisites and corequisites
Basic literature
Slovák J., Lineární algebra, Masarykova univerzita, http://www.math.muni.cz/~slovak/ftp/lectures/linearni.algebra/
Recommended reading
eLearning
Classification of course in study plans
specialization NADE , any year of study, winter semester, electivespecialization NBIO , any year of study, winter semester, electivespecialization NGRI , any year of study, winter semester, electivespecialization NNET , any year of study, winter semester, electivespecialization NVIZ , any year of study, winter semester, electivespecialization NCPS , any year of study, winter semester, electivespecialization NSEC , any year of study, winter semester, electivespecialization NEMB do 2021/22 , any year of study, winter semester, electivespecialization NEMB , any year of study, winter semester, electivespecialization NHPC , any year of study, winter semester, electivespecialization NISD , any year of study, winter semester, electivespecialization NIDE , any year of study, winter semester, electivespecialization NISY do 2020/21 , any year of study, winter semester, electivespecialization NISY , any year of study, winter semester, electivespecialization NMAL , any year of study, winter semester, compulsoryspecialization NMAT , any year of study, winter semester, electivespecialization NSEN , any year of study, winter semester, electivespecialization NVER , any year of study, winter semester, electivespecialization NSPE , any year of study, winter semester, compulsory
Lecture
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
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
Seminars with computer support are organized according to current needs. They enables students to solve algorithmizable problems by computer algebra systems.