|
|
Main menu for Browse IS/STAG
Course info
KMA / LA-A
:
Course description
Department/Unit / Abbreviation
|
KMA
/
LA-A
|
Academic Year
|
2023/2024
|
Academic Year
|
2023/2024
|
Title
|
Linear Algebra
|
Form of course completion
|
Exam
|
Form of course completion
|
Exam
|
Accredited / Credits
|
Yes,
5
Cred.
|
Type of completion
|
Combined
|
Type of completion
|
Combined
|
Time requirements
|
Lecture
3
[Hours/Week]
Tutorial
1
[Hours/Week]
|
Course credit prior to examination
|
Yes
|
Course credit prior to examination
|
Yes
|
Automatic acceptance of credit before examination
|
No
|
Included in study average
|
YES
|
Language of instruction
|
English
|
Occ/max
|
|
|
|
Automatic acceptance of credit before examination
|
No
|
Summer semester
|
0 / -
|
0 / -
|
0 / -
|
Included in study average
|
YES
|
Winter semester
|
0 / -
|
0 / -
|
0 / -
|
Repeated registration
|
NO
|
Repeated registration
|
NO
|
Timetable
|
Yes
|
Semester taught
|
Winter semester
|
Semester taught
|
Winter semester
|
Minimum (B + C) students
|
1
|
Optional course |
Yes
|
Optional course
|
Yes
|
Language of instruction
|
English
|
Internship duration
|
0
|
No. of hours of on-premise lessons |
|
Evaluation scale |
1|2|3|4 |
Periodicity |
každý rok
|
Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
|
Fundamental theoretical course |
No
|
Fundamental course |
No
|
Fundamental theoretical course |
No
|
Evaluation scale |
1|2|3|4 |
Evaluation scale for credit before examination |
S|N |
Substituted course
|
None
|
Preclusive courses
|
KMA/LA and KMA/LAA
|
Prerequisite courses
|
N/A
|
Informally recommended courses
|
N/A
|
Courses depending on this Course
|
N/A
|
Histogram of students' grades over the years:
Graphic PNG
,
XLS
|
Course objectives:
|
The course is intended as an introduction to linear algebra.
|
Requirements on student
|
Credit requirements: one test - 45 min., minimal result 50%
Exam: - test - 90 min., minimal result 40%
orals - two randomly chosen topics of the following ones:
1. polynomials, Horner scheme, polynomial factorization
2. determinant of a matrix, definition and basic properties
3. determinant expansion along a row or a column
4. vector space, linear dependence and independence
5. basis and dimension of a vector space, coordinates of a vector relative to a basis
6. rank of a matrix, Gaussian elimination, calculation of the rank using determinants
7. matrix inverse, Gauss-Jordan elimination
8. calculation of the matrix inverse using determinants
9. linear map (transformation), kernel and image and their dimensions
10. associated matrix of a linear map and its properties
11. inverse linear map, linear map composition and associated matrix
12. vector space isomorphism
13. homogeneous system of linear equations
14. nonhomogeneous system of linear equations
15. linear systems with an invertible matrix coefficient, Cramer's rule
16. eigenvalues and eigenvectors of a matrix
17. change of basis and change-of-basis matrix
18. change of a change-of-basis matrix by change of basis
19. similarity of matrices and its properties, Jordan normal form of a matrix
20. inner product and its properties, norm induced by the inner product
21. orthogonal and orthonormal basis for a space, the Gram-Schmidt process
22. orthogonal projection of a vector on a subspace, method of least squares
23. quadratic forms and real valued symmetric matrices
24. inertia of a quadratic form, Sylvester's law of inertia for quadratic forms
|
Content
|
1. polynomials, Horner scheme, polynomial factorization
2. determinant of a matrix, definition and basic properties, determinant expansion along a row or a column
3. vector space, linear dependence and independence, basis and dimension of a vector space, coordinates of a vector relative to a basis
4. rank of a matrix, Gaussian elimination, calculation of the rank using determinants
5. matrix inverse, Gauss-Jordan elimination, calculation of the matrix inverse using determinants
6. linear map (transformation), kernel and image and their dimensions, associated matrix of a linear map and its properties
7. inverse linear map, linear map composition and associated matrix, vector space isomorphism, change of basis and change-of-basis matrix
8. systems of linear equations, homogeneous and nonhomogeneous systems of equations, linear systems with an invertible matrix coefficient, Cramer's rule
9. eigenvalues and eigenvectors of a matrix, similarity of matrices and its properties, Jordan normal form of a matrix
10. inner product and its properties, norm induced by the inner product, orthogonal and orthonormal basis for a space
11. the Gram-Schmidt process, orthogonal projection of a vector on a subspace
12. method of least squares, quadratic forms and real valued symmetric matrices
13. inertia of a quadratic form, Sylvester's law of inertia for quadratic forms
|
Activities
|
|
Fields of study
|
|
Guarantors and lecturers
|
|
Literature
|
|
Time requirements
|
All forms of study
|
Activities
|
Time requirements for activity [h]
|
Preparation for formative assessments (2-20)
|
25
|
Contact hours
|
52
|
Preparation for an examination (30-60)
|
56
|
Total
|
133
|
|
Prerequisites
|
Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
High school level mathematical skills are assumed. |
|
Learning outcomes
|
Knowledge - knowledge resulting from the course: |
A student will be able to
- find roots of several types of polynomials,
- use the concept of a vector and a matrix,
- calculate determinant of a square matrix and to find its inverse,
- solve algebraic systems of linear equations,
- define and verify a vector space structure,
- work with the concept of a linear map,
- find eigenvalues and eigenvectors of a square matrix and to interpret them geometricaly,
- clasify quadric surfaces,
- approximate functions (data) by the method of least squares.
|
|
Assessment methods
|
Knowledge - knowledge achieved by taking this course are verified by the following means: |
Combined exam |
Test |
Skills demonstration during practicum |
|
Teaching methods
|
Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture |
Interactive lecture |
Practicum |
|
|
|
|