Linear Algebra 1

Garant předmětu:

Karel Klouda

Lecturer:

Marzieh Forough, Antonella Marchesiello

Tutor:

Marzieh Forough, Antonella Marchesiello, Irena Šindelářová

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/BIE-LA1

Time-table for winter semester 2022/2023:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
Wed	roomT9:111 Forough M. 07:30–09:00 (lecture parallel1) Dejvice PosluchárnaroomT9:346 Forough M. 09:15–10:45 (lecture parallel1 parallel nr.101) Dejvice NBFIT učebnaroomTH:A-1442 Forough M. 14:30–16:00 (lecture parallel1 parallel nr.102) Thákurova 7 (FSv-budova A)roomTH:A-1442 Šindelářová I. 16:15–17:45 (lecture parallel1 parallel nr.103) Thákurova 7 (FSv-budova A)
Thu
Fri

Time-table for summer semester 2022/2023:

Time-table is not available yet

The course is a part of the following study plans:

• Bachelor specialization, Computer Engineering, 2021 (compulsory course in the program)
• Bachelor specialization, Information Security, 2021 (compulsory course in the program)
• Bachelor specialization, Software Engineering, 2021 (compulsory course in the program)
• Bachelor specialization, Computer Science, 2021 (compulsory course in the program)
• Bachelor specialization, Computer Networks and Internet, 2021 (compulsory course in the program)
• Bachelor specialization Computer Systems and Virtualization, 2021 (compulsory course in the program)