Linear Algebra

B232 - Summer 23/24
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Linear Algebra - B0B01LAG

Credits 8
Semesters Winter
Completion Assessment + Examination
Language of teaching Czech
Extent of teaching 4P+2S
The course covers the initial parts of linear algebra. Firstly, the basic notions of a linear space and linear mappings are covered (linear dependence and independence, basis, coordinates, etc). The calculus of matrices (determinants, inverse matrices, matrices of a linear map, eigenvalues and eigenvectors, diagonalisation, etc) is covered next. The applications include solving systems of linear equations, the geometry of a 3D space (including the scalar product and the vector product) and SVD.
Course outlines
1. Linear spaces.
2. Linear span, linear dependence and independence.
3. Basis, dimensions, coordinates w.r.t. a basis.
4. Linear mappings, matrices as linear mappings.
5. The matrix of a linear mapping, transformatio of coordinates.
6. Systems of linear equations, Frobenius' Theorem, geometry of solutions of systems.
7. The determinant of a square matrix.
8. Eigenvalues and diagonalisation, Jordan's form.
9. The abstract scalar product.
10. Orthogonal projections and orthogonalisation.
11. Least squares, SVD and pseudoinverse.
12. Mutual position of affine subspaces and their mutual distance.
13. Vector product and metric calculations in R^n.
14. Spare week.
[1] Halmos, P.: Finite-dimensional vector spaces,2nd edition, Springer 2000.
[2] Strang, G.: Introduction to linear algebra, 5th edition, Wellesley-Cambridge 2016.