Course detail
Linear Algebra
FSI-SLAAcad. year: 2020/2021
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.
Guarantor
Department
Learning outcomes of the course unit
Prerequisites
Co-requisites
Recommended optional programme components
Literature
Howard, A. A.: Elementary Linear Algebra, Wiley 2002.
Rektorys, K. a spol.: Přehled užité matematiky I., II., Prometheus 1995.
Searle, S. R.: Matrix Algebra Useful for Statistics, Wiley 1982.
Karásek, J., Skula, L.: Algebra a geometrie, Cerm 2002.
Nedoma, J.: Matematika I., Cerm 2001.
Nedoma, J.: Matematika I., část první: Algebra a geometrie, PC-DIR 1998.
Horák, P., Janyška, J.: Analytická geometrie, Masarykova univerzita 1997.
Janyška, J., Sekaninová, A.: Analytická teorie kuželoseček a kvadrik, Masarykova univerzita 1996.
Mezník, I., Karásek, J., Miklíček, J.: Matematika I. pro strojní fakulty, SNTL 1992.
Horák, P.: Algebra a teoretická aritmetika, Masarykova univerzita 1991.
Procházka, L. a spol.: Algebra, Academia 1990.
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
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
Work placements
Aims
thinking.
Specification of controlled education, way of implementation and compensation for absences
Classification of course in study plans
- Programme B-MAI-P Bachelor's, 1. year of study, winter semester, 6 credits, compulsory
- Programme MITAI Master's
specialization NADE , any year of study, winter semester, 6 credits, elective
specialization NBIO , any year of study, winter semester, 6 credits, elective
specialization NGRI , any year of study, winter semester, 6 credits, elective
specialization NNET , any year of study, winter semester, 6 credits, elective
specialization NVIZ , any year of study, winter semester, 6 credits, elective
specialization NCPS , any year of study, winter semester, 6 credits, elective
specialization NSEC , any year of study, winter semester, 6 credits, elective
specialization NEMB , any year of study, winter semester, 6 credits, elective
specialization NHPC , any year of study, winter semester, 6 credits, elective
specialization NISD , any year of study, winter semester, 6 credits, elective
specialization NIDE , any year of study, winter semester, 6 credits, elective
specialization NISY , any year of study, winter semester, 6 credits, elective
specialization NMAL , any year of study, winter semester, 6 credits, compulsory
specialization NMAT , any year of study, winter semester, 6 credits, elective
specialization NSEN , any year of study, winter semester, 6 credits, elective
specialization NVER , any year of study, winter semester, 6 credits, elective
specialization NSPE , any year of study, winter semester, 6 credits, compulsory
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
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
Teacher / Lecturer
Syllabus
Following weeks: Seminar related to the topic of the lecture given in the previous week.
Computer-assisted exercise
Teacher / Lecturer
Syllabus