CTU FEE Moodle

The course covers introductory topics of linear algebra. It begins with fundamental concepts related to vector spaces and linear transform (such as linear dependence and independence of vectors, bases, coordinates of vectors, etc.). The next part of the course is devoted to matrix theory (determinants, inverse matrix, matrices of linear transformation, eigenvalues and eigenvectors). Applications include solving systems of linear equations, geometry in three-dimensional space (including dot and cross products), and the singular value decomposition of a matrix.

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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.

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[1] Halmos, P.: Finite-dimensional vector spaces,2nd edition, Springer 2000.

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