CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2024/2025

Linear Algebra 1

Code Completion Credits Range Language
BI-LA1.21 Z,ZK 5 2P+1R+1C Czech
Vztahy:
It is not possible to register for the course BI-LA1.21 if the student is concurrently registered for or has already completed the course BI-LIN (mutually exclusive courses).
The requirement for course BI-LA1.21 can be fulfilled by substitution with the course BI-LIN.
It is not possible to register for the course BI-LA1.21 if the student is concurrently registered for or has previously completed the course BI-LIN (mutually exclusive courses).
Garant předmětu:
Karel Klouda
Lecturer:
Luděk Kleprlík, Karel Klouda, Jakub Krásenský
Tutor:
Luděk Kleprlík, Karel Klouda, Jakub Krásenský, Marta Nollová, Hanka Řada, Lucie Strmisková
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 non-parametric 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 non-parametric 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). Wellesley-Cambridge Press, 2016. ISBN 978-0980232776.

2. Lay D.C., Lay S.R., McDonald J.J. : Linear Algebra and Its Applications (5th Edition). Pearson, 2015. ISBN 978-0321982384.

3. Axler S. : Linear Algebra Done Right (3rd Edition). Springer, 2014. ISBN 978-3319110790.

4. Klein P. N. : Coding the Matrix: Linear Algebra through Applications to Computer Science. Newtonian Press, 2013. ISBN 978-0615880990.

Note:
Further information:
http://courses.fit.cvut.cz/BI-LA1
Time-table for winter semester 2024/2025:
Time-table is not available yet
Time-table for summer semester 2024/2025:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-06-16
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet6533706.html