# Subject description - A7B01LAG

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 A7B01LAG Linear Algebra Extent of teaching: 2+2 Guarantors: Roles: P Language ofteaching: CS Teachers: Completion: Z,ZK Responsible Department: 13101 Credits: 6 Semester: Z

Anotation:

The course covers introductory topics of linear algebra. They include matrices, matrix operations, inversion of matrices, vector spaces, bases and dimension and their applications to solving systems of linear equations. Vector spaces are presented over real numbers and GF(2). Eigenvalues and eigenvectors of matrices.

Course outlines:

 1 Vector spaces, axioms of linearity. 2 Linear independence, linear dependence, linear span. 3 Basis, dimension, coordinates of vectors. 4 Matrices, operations with matrices. 5 Determinants. 6 Inverse matrices. 7 Systems of linear equations. 8 Linear mappings, matrices of linear mappings. 9 Eigenvalues and eigenvectors of matrices. 10 Scalar product, orthogonality. 11 Arithmetic vectors over GF(2), solution of linear equations over FG(2). 12 Applications in linear coding. 13 Back-up class.

Exercises outline:

 1 Polynomials, roots of polynomials. 2 Gaussian elimination, rank of matrices. 3 Vector spaces, linear independence, linear dependence. 4 Basis, dimension, coordinates of vectors. 5 Matrices, operations with matrices. 6 Determinants. 7 Systems of linear equations. 8 Linear mappings, matrices of linear mappings. 9 Eigenvalues and eigenvectors of matrices. 10 Scalar product, orthogonality. 11 Arithmetic vectors over GF(2), solution of linear equations over FG(2). 12 Applications in linear coding. 13 Back-up class.

Literature:

 1 P. Pták: Introduction to Linear Algebra. ČVUT, Praha, 2005. 2 P. Pták: Introduction to Linear Algebra, starší vydání přístupné elektronicky.

Requirements:

To be specified in seminars by tutors.

Webpage:

http://math.feld.cvut.cz/velebil/teaching/a7b01lag.html

Subject is included into these academic programs:

 Program Branch Role Recommended semester BPSTM_BO Common courses P 1 BPSTMWM Web and Multimedia P 1 BPSTMSI Software Engineering P 1 BPSTMMI Manager Informatics P 1 BPSTMIS Intelligent Systems P 1

 Page updated 13.12.2019 14:52:09, semester: Z,L/2020-1, L/2018-9, Z,L/2019-20, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)