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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

Linear Algebra 1

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Code Completion Credits Range Language
BI-LA1.21 Z,ZK 5 2P+1R+1C Czech
The course cannot be taken simultaneously with:
Linear Algebra (BI-LIN)
Garant předmětu:
Karel Klouda
Lecturer:
Luděk Kleprlík, Karel Klouda, Jakub Krásenský
Tutor:
Daniel Dombek, Luděk Kleprlík, Karel Klouda, Jakub Krásenský, Marta Nollová, Petr Pauš, Hanka Řada, Jan Starý, Lucie Strmisková, Jaroslav Zhouf
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 2023/2024:
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
roomTH:A-1442

09:15–10:00
(parallel nr.1)
Thákurova 7 (budova FSv)
roomTH:A-1442

10:00–10:45
(parallel nr.2)
Thákurova 7 (budova FSv)
roomTH:A-1442

11:00–11:45
(parallel nr.3)
Thákurova 7 (budova FSv)
roomTH:A-1442

11:45–12:30
(parallel nr.4)
Thákurova 7 (budova FSv)
roomT9:347

14:30–15:15
(parallel nr.5)
Dejvice
NBFIT učebna
roomT9:347

15:15–16:00
(parallel nr.6)
Dejvice
NBFIT učebna
roomTH:A-1242

16:15–17:00
(parallel nr.11)
Thákurova 7 (budova FSv)
roomTH:A-1242

17:00–17:45
(parallel nr.12)
Thákurova 7 (budova FSv)
roomTH:A-1242

18:00–18:45
(parallel nr.13)
Thákurova 7 (budova FSv)
roomTH:A-1242

18:45–19:30
(parallel nr.14)
Thákurova 7 (budova FSv)
roomT9:301

14:30–15:15
(parallel nr.7)
Dejvice
NBFIT učebna
roomT9:301

15:15–16:00
(parallel nr.8)
Dejvice
NBFIT učebna
Tue
roomT9:302

12:45–13:30
(parallel nr.15)
Dejvice
NBFIT učebna
roomTH:D-1122
Klouda K.
14:30–16:00
(lecture parallel1)
Thákurova 7 (budova FSv)
D1122
roomT9:105
Kleprlík L.
18:00–19:30
(lecture parallel2)
Dejvice
Posluchárna
roomT9:302

13:30–14:15
(parallel nr.16)
Dejvice
NBFIT učebna
roomT9:302

14:30–15:15
(parallel nr.17)
Dejvice
NBFIT učebna
roomT9:302

15:15–16:00
(parallel nr.18)
Dejvice
NBFIT učebna
roomT9:302

16:15–17:00
(parallel nr.19)
Dejvice
NBFIT učebna
roomT9:302

17:00–17:45
(parallel nr.20)
Dejvice
NBFIT učebna
Wed
roomTH:A-1442

09:15–10:00
(parallel nr.21)
Thákurova 7 (budova FSv)
roomTH:A-1442

18:00–18:45
(parallel nr.9)
Thákurova 7 (budova FSv)
roomTH:A-1442

18:45–19:30
(parallel nr.10)
Thákurova 7 (budova FSv)
roomTH:A-1442

10:00–10:45
(parallel nr.22)
Thákurova 7 (budova FSv)
roomTH:A-1442

11:00–11:45
(parallel nr.23)
Thákurova 7 (budova FSv)
roomTH:A-1442

11:45–12:30
(parallel nr.24)
Thákurova 7 (budova FSv)
roomTH:A-1442

12:45–13:30
(parallel nr.25)
Thákurova 7 (budova FSv)
roomTH:A-1442

13:30–14:15
(parallel nr.26)
Thákurova 7 (budova FSv)
roomTH:A-1442

14:30–15:15
(parallel nr.27)
Thákurova 7 (budova FSv)
roomTH:A-1442

15:15–16:00
(parallel nr.28)
Thákurova 7 (budova FSv)
roomTH:A-1442

16:15–17:00
(parallel nr.29)
Thákurova 7 (budova FSv)
roomTH:A-1442

17:00–17:45
(parallel nr.30)
Thákurova 7 (budova FSv)
roomT9:155
Krásenský J.
11:00–12:30
(lecture parallel3)
Dejvice
Posluchárna
Thu
roomTH:A-1247

09:15–10:00
(parallel nr.31)
Thákurova 7 (budova FSv)
seminární místnost
roomTH:A-1247

10:00–10:45
(parallel nr.32)
Thákurova 7 (budova FSv)
seminární místnost
roomTH:A-1247

11:00–11:45
(parallel nr.33)
Thákurova 7 (budova FSv)
seminární místnost
roomTH:A-1247

11:45–12:30
(parallel nr.34)
Thákurova 7 (budova FSv)
seminární místnost
Fri
roomT9:302

09:15–10:00
(parallel nr.35)
Dejvice
NBFIT učebna
roomT9:302

10:00–10:45
(parallel nr.36)
Dejvice
NBFIT učebna
roomT9:302

11:00–11:45
(parallel nr.37)
Dejvice
NBFIT učebna
roomT9:302

11:45–12:30
(parallel nr.38)
Dejvice
NBFIT učebna
Time-table for summer semester 2023/2024:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2023-08-30
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet6533706.html