Linear Algebra

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Linear Algebra (Main course) BE5B01LAL
Credits 8
Semesters Winter
Completion Assessment + Examination
Language of teaching English
Extent of teaching 4P+2S
Annotation
The course covers standard basics of matrix calculus (determinants, inverse matrix) and linear algebra (basis, dimension, inner product spaces, linear transformations) including eigenvalues and eigenvectors. Matrix similarity, orthogonal bases, and bilinear and quadratic forms are also covered.
Course outlines
1. Polynomials. Introduction to systems of linear equations and Gauss elimination method.
2. Linear spaces, linear dependence and independence.
3. Basis, dimension, coordinates of vectors.
4. Matrices: operations, rank, transpose.
5. Determinant and inverse of a matrix.
6. Structure of solutions of systems of linear equations. Frobenius Theorem.
7. Linear mappings. Matrix of a linear mapping.
8. Free vectors. Dot product and cross product.
9. Lines and planes in 3-dimensional real space.
10. Eigenvalues and eigenvectors of matrices and linear mappings.
11. Similarity of matrices, matrices similar to diagonal matrices.
12. Euclidean space, orthogonalization, orthonormal basis. Fourier basis.
13. Introduction to bilinear and quadratic forms.
Exercises outlines
1. Polynomials. Introduction to systems of linear equations and Gauss elimination method.
2. Linear spaces, linear dependence and independence.
3. Basis, dimension, coordinates of vectors.
4. Matrices: operations, rank, transpose.
5. Determinant and inverse of a matrix.
6. Structure of solutions of systems of linear equations. Frobenius Theorem.
7. Linear mappings. Matrix of a linear mapping.
8. Free vectors. Dot product and cross product.
9. Lines and planes in 3-dimensional real space.
10. Eigenvalues and eigenvectors of matrices and linear mappings.
11. Similarity of matrices, matrices similar to diagonal matrices.
12. Euclidean space, orthogonalization, orthonormal basis. Fourier basis.
13. Introduction to bilinear and quadratic forms.
Literature
1. P. Pták: Introduction to Linear Algebra. ČVUT, Praha, 2005.
2. P. Pták: Introduction to Linear Algebra. ČVUT, Praha, 1997.

https://math.fel.cvut.cz/en/people/vivipaol/LAL2015.pdf
Requirements
https://math.fel.cvut.cz/en/people/vivipaol/LAL2015.pdf