|
Lecturer(s)
|
-
Marek Josef, doc. Ing. Ph.D.
|
|
Course 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
|
|
Learning activities and teaching methods
|
Interactive lecture, Lecture, Practicum
- Preparation for formative assessments (2-20)
- 25 hours per semester
- Preparation for an examination (30-60)
- 56 hours per semester
- Contact hours
- 52 hours per semester
|
| prerequisite |
|---|
| Knowledge |
|---|
| High school level mathematical skills are assumed. |
| learning outcomes |
|---|
| 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. |
| teaching methods |
|---|
| Lecture |
| Interactive lecture |
| Practicum |
| assessment methods |
|---|
| Combined exam |
| Test |
| Skills demonstration during practicum |
|
Recommended literature
|
-
Banchoff, Thomas; Wermer, John. Linear algebra through geometry. Springer, 1992. ISBN 978-0-387-97586-3.
-
Edwards, Harold M. Linear algebra. New York : Birkhäuser, 1995. ISBN 0-8176-3731-1.
-
Lang, Serge. Introduction to linear algebra. New York : Springer-Verlag, 1986. ISBN 0-387-96205-0.
|