Course details

# Linear Algebra

ILG Acad. year 2023/2024 Winter semester 5 credits

Matrices and determinants. Systems of linear equations. Vector spaces and subspaces. Linear representation, coordinate transformation. Own values and own vectors. Quadratic forms and conics.

Guarantor

Course coordinator

Language of instruction

Czech, English

Completion

Credit+Examination (written)

Time span

• 26 hrs lectures
• 26 hrs exercises

Assessment points

• 80 pts final exam
• 20 pts numeric exercises

Department

Lecturer

Instructor

Learning objectives

The students will get familiar with elementary knowledge of linear algebra, which is needed for informatics applications. Emphasis is placed on mastering the practical use of this knowledge to solve specific problems.
The students will acquire an elementary knowledge of linear algebra and the ability to apply some of its basic methods in computer science.

Why is the course taught

Linear algebra is one of the most important branches of mathematics for engineers, regardless of their specialization, as it deals with both specific computational procedures and abstract concepts, which are useful for describing technical problems. The knowledge gained in the course is applied by graduates where engineering problems are written in  matrices, vectors and linear equations. The mastering of the basic concepts and their context will facilitate for further study and development of the chosen field.

Prerequisite knowledge and skills

Secondary school mathematics.

Study literature

• Havel, V., Holenda, J., Lineární algebra, STNL, Praha 1984.
• Kolman B., Elementary Linear Algebra, Macmillan Publ. Comp., New York 1986.

Syllabus of lectures

1. Systems of linear homogeneous and non-homogeneous equations. Gaussian elimination.
2. Matrices and matrix operations. Rank of the matrix. Frobenius theorem.
3. The determinant of a square matrix. Inverse and adjoint matrices. The methods of computing the determinant.The Cramer's Rule.
4. The vector space and its subspaces. The basis and the dimension. The coordinates of a vector relative to a given basis. The sum and intersection of vector spaces.
5. The inner product. Orthonormal systems of vectors. Orthogonal projection and approximation. Gram-Schmidt orthogonalisation process.
6. The transformation of the coordinates.
7. Linear mappings of vector spaces. Matrices of linear transformations.
8. Rotation, translation, symmetry and their matrices, homogeneous coordinates.
9. The eigenvalues and eigenvectors. The orthogonal projections onto eigenspaces.
10. Numerical solution of systems of linear equations, iterative methods.
11. Conic sections.
12. Quadratic forms and their classification using sections.
13. Quadratic forms and their classification using eigenvectors.

Syllabus of numerical exercises

Examples of tutorials are chosen to suitably complement the lectures.

Progress assessment

• Evaluation of the five written tests (max 20 points).

• Participation in lectures in this course is not controlled.
• The knowledge of students is tested at exercises  at five written tests for 4 points each and at the final exam for 80 points.
• If a student can substantiate serious reasons for an absence from an exercise, (s)he can either attend the exercise with a different group (please inform the teacher about that) or ask his/her teacher for an alternative assignment to compensate for the lost points from the exercise.
• The passing boundary for ECTS assessment: 50 points.

Exam prerequisites

The minimal total score of 8 points gained out of the mid-term exams.

Schedule

DayTypeWeeksRoomStartEndCapacityLect.grpGroupsInfo
Mon exercise 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures A113 08:0009:5064 1BIA 1BIB 2BIA 2BIB xx Pekárková
Mon exercise 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures A113 10:0011:5064 1BIA 1BIB 2BIA 2BIB xx Pekárková
Mon exercise 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures A113 12:0013:5064 1BIA 1BIB 2BIA 2BIB xx Pekárková
Tue exam 2023-12-19 D0206 D105 09:0011:50 Předtermín
Tue exercise 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures T8/T 3.12 09:0010:5056 1BIA 1BIB 2BIA 2BIB xx Hlavičková
Tue lecture lectures Aula profesora Braunera 13:0014:50338 1BIB 2BIA 2BIB 30 - 49 xx Hlavičková
Tue exam 2024-01-23 D0206 D0207 D105 13:3015:50 2. termín
Wed exercise 1., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures A112 09:0010:5064 1BIA 1BIB 2BIA 2BIB xx Vévodová
Wed exercise 1., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures A112 11:0012:5064 1BIA 1BIB 2BIA 2BIB xx Vévodová
Wed lecture lectures D0207 D105 12:0013:509999 1BIA 2BIA 2BIB 10 - 29 xx Hliněná
Wed exercise 1., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures A112 13:0014:5064 1BIA 1BIB 2BIA 2BIB xx Vévodová
Wed exercise 1., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures A113 15:0016:5064 1BIA 1BIB 2BIA 2BIB xx Vítovec
Thu exercise 1., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures D0207 12:0013:5064 1BIA 1BIB 2BIA 2BIB xx Vítovec
Thu exercise 1., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures T8/T 3.02 13:0014:5056 1BIA 1BIB 2BIA 2BIB xx Hlavičková
Thu exercise 1., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures D0207 14:0015:5064 1BIA 1BIB 2BIA 2BIB xx Vítovec
Fri exercise 1., 2., 3., 4., 5., 6., 7., 8., 10., 11., 12., 13. of lectures A113 08:0009:5064 1BIA 1BIB 2BIA 2BIB xx Hliněná
Fri exercise 1., 2., 3., 4., 5., 6., 7., 8., 10., 11., 12., 13. of lectures A113 10:0011:5064 1BIA 1BIB 2BIA 2BIB xx Hliněná
Fri exam 2024-01-12 D0206 D0207 D105 13:3015:50 řádná
Fri exam 2024-02-02 Aula profesora Kalendovského T8/T 0.10 T8/T 0.30 13:3015:50 3. termín

Course inclusion in study plans

• Programme BIT, 1st year of study, Compulsory
• Programme BIT (in English), 1st year of study, Compulsory
• Programme IT-BC-3, field BIT, 1st year of study, Compulsory