Linear Algebra
Code  Completion  Credits  Range  Language 

B01LAG  Z,ZK  6  2+2  Czech 
 Lecturer:
 Tutor:
 Supervisor:
 Department of Mathematics
 Synopsis:

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.
 Requirements:

To be specified in seminars by tutors.
 Syllabus of lectures:

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. Backup class.
 Syllabus of tutorials:

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. Backup class.
 Study Objective:
 Study materials:

1. P. Pták: Introduction to Linear Algebra. ČVUT, Praha, 2005.
2. P. Pták: Introduction to Linear Algebra, starší vydání přístupné elektronicky.
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans: