# Subject description - BE5B01LAL

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BE5B01LAL Linear Algebra
Roles:P Extent of teaching:4P+2S
Department:13101 Language of teaching:EN
Guarantors:Vivi P. Completion:Z,ZK
Lecturers:Vivi P. Credits:8
Tutors:Vivi P. Semester:Z

Anotation:

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 outline:

 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

Webpage:

https://math.fel.cvut.cz/en/people/vivipaol/BE5B01LAL.html

Subject is included into these academic programs:

 Program Branch Role Recommended semester BPEECS_2018 Common courses P 1 BEECS Common courses P 1

 Page updated 29.9.2022 05:51:42, semester: Z,L/2022-3, Z/2024-5, L/2021-2, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)