Linear algebra 1000-711ALI
1. Gauss elimination method
2. Matrix algebra
3. Matrix form of systems of equations (LDU decomposition of a matrix, Gauss-Jordan method of determining the inverse matrix)
4. Linear spaces (fundamental subspaces related to matrices, linear independence of vectors,
base and dimension of a linear space, rank of a matrix)
5. Orthogonality (projection of a vector on a line and on a subspace, orthogonal complement of space,
least squares method, Gram-Schmidt orthogonalization)
6. Matrix determinant (axiomatic definition, Laplace expansion, Cramer's formulas, calculation of the volume of solids)
7. Eigenvalues and eigenvectors (remarks about complex numbers, matrix diagonalization,
exponentiation and exponential function of a matrix, spectral decomposition of a symmetric matrix, principal component analysis)
8. Singular value decomposition of matrices (positive definite and positive semidefinite matrices, SVD decomposition)
Type of course
Course coordinators
Learning outcomes
Knowledge:
- has basic knowledge of combinatorics, graph theory and linear algebra
Skills:
- uses appropriate software packages to perform calculations on matrices
Assessment criteria
Written exam (60%), colloquium (40%).
Bibliography
* Linear Algebra and Its Applications, 4th Edition, R. Strang, Cengage Learning, 2005
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
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