470-2205/03 – Linear Algebra (LA)
| Gurantor department | Department of Applied Mathematics | Credits | 7 |
| Subject guarantor | doc. Ing. Petr Beremlijski, Ph.D. | Subject version guarantor | doc. Ing. Petr Beremlijski, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2019/2020 | Year of cancellation | |
| Intended for the faculties | FS, FEI | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
To supply working knowledge of basic concepts of linear algebra including their geometric and computational meaning, in order to enable to use these concepts in solution of basic problems of linear algebra. Student should also learn how to use the basic tools of linear algebra in applications.
Teaching methods
Lectures
Tutorials
Summary
Linear algebra is one of the basic tools of formulation and solution of engineering problems. The students will get in an elementary way basic concepts and comutational skills of linear algebra, including algorithmic aspects that are important in computer implementation.
Compulsory literature:
H. Anton, Elementary Linear Algebra, J. Wiley , New York 1991
Recommended literature:
S. Barnet, Matrices, Methods and Applications, Clarendon Press, Oxford 1994
H. Schnaider, G. P. Barker, Matrices and Linear Algebra, Dover, New York 1989
Way of continuous check of knowledge in the course of semester
Verification of study:
4 tests on solution of linear systems, matrix algebra, vector spaces, linear mapping and multilinear algebra (max 24m, min 10m)
Project (max 6m, min 0m)
Conditions for credit:
Minimum 10 marks on tests and project.
E-learning
https://homel.vsb.cz/~ber95/LA_VAM/la.htm
Other requirements
No additional requirements are imposed on the student.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Lectures:
An introduction to matrix calculus
Solution of systems of linear equations
Inverse matrices and LU factorization
Vector spaces and subspaces
Basis and dimension of vector spaces
Linear mapping
Bilinear and quadratic forms
Scalar product
Determinants
Eigenvalues and eigenvectors
Linear algebra applications
Exercises:
Practicing algebra of arithmetic vectors and matrices
Solution of systems of linear equations
Evaluation of inverse matrix
LU factorization
Examples of vector spaces and deduction from axioms
Evaluation of coordinates of a vector in a given basis
Examples of linear mappings and evaluation of their matrices
Matrices of bilinear and quadratic forms
Orthogonalization process
Evaluation of determinants
Evaluation of eigenvalues and eigenvectors
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction