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A course is the basic teaching unit, it's design as a medium for a student to acquire comprehensive knowledge and skills indispensable in the given field. A course guarantor is responsible for the factual content of the course.
For each course, there is a department responsible for the course organisation. A person responsible for timetabling for a given department sets a time schedule of teaching and for each class, s/he assigns an instructor and/or an examiner.
Expected time consumption of the course is expressed by a course attribute extent of teaching. For example, extent = 2 +2 indicates two teaching hours of lectures and two teaching hours of seminar (lab) per week.
At the end of each semester, the course instructor has to evaluate the extent to which a student has acquired the expected knowledge and skills. The type of this evaluation is indicated by the attribute completion. So, a course can be completed by just an assessment ('pouze zápočet'), by a graded assessment ('klasifikovaný zápočet'), or by just an examination ('pouze zkouška') or by an assessment and examination ('zápočet a zkouška') .
The difficulty of a given course is evaluated by the amount of ECTS credits.
The course is in session (cf. teaching is going on) during a semester. Each course is offered either in the winter ('zimní') or summer ('letní') semester of an academic year. Exceptionally, a course might be offered in both semesters.
The subject matter of a course is described in various texts.

BI-LA2.21 Linear Algebra 2 Extent of teaching: 2P+2C

Instructor: Šístek J., Kleprlík L., Klouda K. Completion: Z,ZK

Department: 18105 Credits: 5 Semester: L

Annotation:
Studenti si v tomto předmětu rozšíří znalosti z předmětu BI-LA1, kde se pracovalo pouze s vektory ve formě n-tic čísel. Zde si zavedeme vektorový prostor v abstraktní obecné formě. Seznámíme se také s pojmem skalární součin a lineární zobrazení, což nám dovolí ukázat souvislost s lineární algebrou, geometrií a počítačovou grafikou. Dalším velkým tématem bude numerická lineární algebra, kde si ukážeme potíže s řešením soustav lineárních rovnic na počítači a možnosti, jak se s tímto problémem vypořádat s důrazem na rozklady matic. Ukážeme si také aplikace lineární algebry v různých oborech.

Lecture syllabus:

1. Abstract vector spaces, infinite-dimensional vector spaces.

2. Scalar products, vector norm, orthogonality.

3. Scalar products and analytical geometry.

4. [2] Linear maps and their matrices.

6. Affine transformations, homogeneous coordinates, projections and operations in 3D space as linear maps.

7. Introduction to numerical mathematics.

8. Solving systems of linear equations on computers.

9. [2] Matrix factorizations (LU, SVD, QR): computation and applications.

11. [3] Applications of linear algebra: the least-squares method, linear programming, recurrent equations.

Seminar syllabus:

1. Abstract vector spaces.

2. Scalar products, vector norm, orthogonality.

3. Analytical geometry.

4. Linear maps.

5. Matrices of linear maps.

6. [2] Affine transformations, homogeneous coordinates, projections and operations in 3D space as linear maps.

8. Systems of linear equations.

9. [2] Matrix factorizations (LU, SVD, QR).

11. The least-squares method.

12. Linear programming.

13. Recurrent equations.

Literature:

1. Lloyd N. T., David B. : Numerical Linear Algebra. SIAM, 1997. ISBN 978-0898713619.

2. Lyche T. : Numerical Linear Algebra and Matrix Factorizations. Springer, 2020. ISBN 978-3030364670.

3. Gentle J. E. : Matrix Algebra: Theory, Computations and Applications in Statistics (2nd Edition). Springer, 2017. ISBN 978-3319648668.

4. Lengyel E. : Mathematics for 3D Game Programming and Computer Graphics (3rd Edition). Cengage Learning PTR, 2011. ISBN 978-1435458864.

Requirements:
We assume the students finished course BI-LA1.21.

http://courses.fit.cvut.cz/BI-LA2

The course is also part of the following Study plans:

Study Plan Study Branch/Specialization Role Recommended semester

BI-TI.21 Computer Science 2021 (in Czech) PS 2

BI-PI.21 Computer Engineering 2021 (in Czech) PS 2

BI-PS.21 Computer Networks and Internet 2021 (in Czech) V 2

BI-WI.21 Web Engineering 2021 (in Czech) V 2

BI-PV.21 Computer Systems and Virtualization 2021 (in Czech) V 2

BI-MI.21 Business Informatics 2021 (In Czech) V 2

BI-UI.21 Artificial Intelligence 2021 (in Czech) PS 2

BI-SPOL.21 Unspecified Branch/Specialisation of Study VO 2

BI-PG.21 Computer Graphics 2021 (in Czech) PS 2

BI-SI.21 Software Engineering 2021 (in Czech) V 2

BI-IB.21 Information Security 2021 (in Czech) V 2

Page updated 23. 4. 2024, semester: Z/2024-5, Z,L/2022-3, Z/2019-20, Z,L/2021-2, Z,L/2023-4, L/2019-20, Z,L/2020-1, Send comments to the content presented here to Administrator of study plans Design and implementation: J. Novák, I. Halaška

BI-LA2.21	Linear Algebra 2			Extent of teaching:	2P+2C
Instructor:	Šístek J., Kleprlík L., Klouda K.			Completion:	Z,ZK
Department:	18105	Credits:	5	Semester:	L

1.		Abstract vector spaces, infinite-dimensional vector spaces.
2.		Scalar products, vector norm, orthogonality.
3.		Scalar products and analytical geometry.
4.		[2] Linear maps and their matrices.
6.		Affine transformations, homogeneous coordinates, projections and operations in 3D space as linear maps.
7.		Introduction to numerical mathematics.
8.		Solving systems of linear equations on computers.
9.		[2] Matrix factorizations (LU, SVD, QR): computation and applications.
11.		[3] Applications of linear algebra: the least-squares method, linear programming, recurrent equations.

1.		Abstract vector spaces.
2.		Scalar products, vector norm, orthogonality.
3.		Analytical geometry.
4.		Linear maps.
5.		Matrices of linear maps.
6.		[2] Affine transformations, homogeneous coordinates, projections and operations in 3D space as linear maps.
8.		Systems of linear equations.
9.		[2] Matrix factorizations (LU, SVD, QR).
11.		The least-squares method.
12.		Linear programming.
13.		Recurrent equations.

1.		Lloyd N. T., David B. : Numerical Linear Algebra. SIAM, 1997. ISBN 978-0898713619.
2.		Lyche T. : Numerical Linear Algebra and Matrix Factorizations. Springer, 2020. ISBN 978-3030364670.
3.		Gentle J. E. : Matrix Algebra: Theory, Computations and Applications in Statistics (2nd Edition). Springer, 2017. ISBN 978-3319648668.
4.		Lengyel E. : Mathematics for 3D Game Programming and Computer Graphics (3rd Edition). Cengage Learning PTR, 2011. ISBN 978-1435458864.