Subject description - B0B01LAG
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Explanatory Notes
Instructions
Web page:
https://moodle.fel.cvut.cz/courses/B0B01LAG
Anotation:
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. |
Exercises outline:
Literature:
| [1] | | Halmos, P.: Finite-dimensional vector spaces,2nd edition, Springer 2000. |
| [2] | | Strang, G.: Introduction to linear algebra, 5th edition, Wellesley-Cambridge 2016. |
Requirements:
Subject is included into these academic programs:
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Proposal and Realization: I. Halaška (K336), J. Novák (K336) |