Linear Algebra Plus
| Code | Completion | Credits | Range | Language |
|---|---|---|---|---|
| 01LAP | Z,ZK | 5 | 1+1 | Czech |
- Grading of the course requires grading of the following courses:
- Linear Algebra 1 (01LA1)
- Lecturer:
- Lubomíra Balková (gar.), Jiří Pytlíček (gar.)
- Tutor:
- Lubomíra Balková (gar.), Jiří Pytlíček (gar.)
- Supervisor:
- Department of Mathematics
- Synopsis:
-
The subject summarizes the most important notions and theorems related to the study of vector spaces.
- Requirements:
- Syllabus of lectures:
-
Vector space - linear independance, basis, dimension, subspace. Linear mapping (linear functional, linear operator) - kernel, rank, defect, matrix of linear mapping. Systems of linear equations - Gauss elimination. Affine subspaces, convex sets.
- Syllabus of tutorials:
-
1. Examples of vector spaces. 2. Investigation of linear dependence/independence-problems with parameters (especially on spaces of polynomials). 3. Selection of basis vectors from a set of generators, completing a basis. 4. Intersection and sum of subspaces - their basis and dimension. 5. Assembling matrices of linear mappings - especially on spaces of polynomials. 6. Linear functionals - dual basis. 7. Systems of linear algebraic equations including systems with parameters. 8. Geometry of linear manifolds, intersection of manifolds, intersection of convex sets and their description using different types of equations.
- Study Objective:
-
Knowledge: Basic concepts of linear algebra. Skills: To be able to use these findings in further studies not only of mathematical disciplines, but also in physics, economics.
- Study materials:
-
Key references:
[1] Linear Algebra with Applications, Prentice-Hall, Inc., Englewood Cliffs, New Jersey,1980
[2] C. W. Curtis : Linear Algebra, An Introductory Approach, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo 1984.
Recommended references:
[3] P. Lancaster : Theory of Matrices, Academic Press, New York, London, 1969.
- Note:
- Time-table for winter semester 2011/2012:
- Time-table is not available yet
- Time-table for summer semester 2011/2012:
- Time-table is not available yet
- The course is a part of the following study plans: