Linear Algebra 1
Code  Completion  Credits  Range  Language 

BIKLA1.21  Z,ZK  5  14KP+4KC  Czech 
 Garant předmětu:
 Karel Klouda
 Lecturer:
 Karel Klouda
 Tutor:
 Karel Klouda
 Supervisor:
 Department of Applied Mathematics
 Synopsis:

We will introduce students to the basic concepts of linear algebra, such as vectors, matrices, vector spaces. We will define vector spaces over the field of real and complex numbers and also over finite fields. We will present the concepts of basis and dimension and learn to solve systems of linear equations using the Gaussian elimination method (GEM) and show the connection with linear manifolds. We define the regularity of matrices and learn to find their inversions using GEM. We will also learn to find eigenvalues and eigenvectors of a matrix. We will also demonstrate some applications of these concepts in computer science.
 Requirements:

The ability to think mathematically and knowledge of a high school mathematics.
 Syllabus of lectures:

1. Fields, vectors, and vector spaces.
2. Matrices, matrix operations and matrix notation of a system of linear equations.
3. Solving systems of linear equations using Gauss elimination method.
4. Linear (in)dependence of vectors, linear span, subspace.
5. Base, dimension of a vector (sub)space.
6. Matrix rank, regularity of a matrix, inverse of matrix and its computation.
7. Frobenius theorem on solutions of a system of linear equations.
9. Linear manifolds, parametric and nonparametric equations of linear manifolds.
10. Permutations, determinant of a matrix.
11. [2] Eigenvalues and eigenvectors of matrices.
13. Diagonalization of matrices.
 Syllabus of tutorials:

1. Matrices, matrix operations. Solving systems of linear equations using Gauss elimination method.
2. Linear (in)dependence of vectors, linear span, subspace. Base, dimension of a vector (sub)space.
3. Matrix rank, regularity of a matrix, inverse of matrix and its computation.
4. Frobenius theorem on solutions of a system of linear equations.
5. Linear manifolds, parametric and nonparametric equations of linear manifolds. Determinant of a matrix.
6. Eigenvalues and eigenvectors of matrices. Diagonalization of matrices.
 Study Objective:
 Study materials:

1 Strang G. : Introduction to Linear Algebra (5th Edition). WellesleyCambridge Press, 2016. ISBN 9780980232776.
2. Lay D.C., Lay S.R., McDonald J.J. : Linear Algebra and Its Applications (5th Edition). Pearson, 2015. ISBN 9780321982384.
3. Axler S. : Linear Algebra Done Right (3rd Edition). Springer, 2014. ISBN 9783319110790.
4. Klein P. N. : Coding the Matrix: Linear Algebra through Applications to Computer Science. Newtonian Press, 2013. ISBN 9780615880990.
 Note:
 Further information:
 http://courses.fit.cvut.cz/BILA1
 Timetable for winter semester 2024/2025:
 Timetable is not available yet
 Timetable for summer semester 2024/2025:
 Timetable is not available yet
 The course is a part of the following study plans:

 Bachelor specialization Information Security, parttime, in Czech, 2021 (compulsory course in the program)
 Bachelor specialization Software Engineering, parttime, in Czech, 2021 (compulsory course in the program)
 Bachelor specialization Computer Networks and Internet, parttime, in Czech, 2021 (compulsory course in the program)
 Bachelor specialization Computer Systems and Virtualization, parttime, in Czech, 2021 (compulsory course in the program)
 Bachelor program, unspecified specialization, parttime, in Czech, 2021 (compulsory course in the program)
The requirement for course BIKLA1.21 can be fulfilled by substitution with the course BIKLIN.