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B0B01LAG	Linear Algebra
Roles:	P	Extent of teaching:	4P+2S
Department:	13101	Language of teaching:	CS
Guarantors:	Velebil J.	Completion:	Z,ZK
Lecturers:	Velebil J.	Credits:	8
Tutors:	Too many persons	Semester:	Z

Web page:

https://moodle.fel.cvut.cz/courses/B0B01LAG

Anotation:

The course covers the initial parts of linear algebra. Firstly, the basic notions of a linear space and linear mappings are covered (linear dependence and independence, basis, coordinates, etc). The calculus of matrices (determinants, inverse matrices, matrices of a linear map, eigenvalues and eigenvectors, diagonalisation, etc) is covered next. The applications include solving systems of linear equations, the geometry of a 3D space (including the scalar product and the vector product) and SVD.

Course outlines:

1.		Linear spaces.
2.		Linear span, linear dependence and independence.
3.		Basis, dimensions, coordinates w.r.t. a basis.
4.		Linear mappings, matrices as linear mappings.
5.		The matrix of a linear mapping, transformatio of coordinates.
6.		Systems of linear equations, Frobenius' Theorem, geometry of solutions of systems.
7.		The determinant of a square matrix.
8.		Eigenvalues and diagonalisation, Jordan's form.
9.		The abstract scalar product.
10.		Orthogonal projections and orthogonalisation.
11.		Least squares, SVD and pseudoinverse.
12.		Mutual position of affine subspaces and their mutual distance.
13.		Vector product and metric calculations in R^n.
14.		Spare week.

Exercises outline:

Literature:

[1]		Halmos, P.: Finite-dimensional vector spaces,2nd edition, Springer 2000.
[2]		Strang, G.: Introduction to linear algebra, 5th edition, Wellesley-Cambridge 2016.

Requirements:

Subject is included into these academic programs:

Program	Branch	Role	Recommended semester
BPOI_BO_2018	Common courses	P	1
BPOI4_2018	Computer Games and Graphics	P	1
BPOI3_2018	Software	P	1
BPOI2_2018	Internet of Things	P	1
BPOI1_2018	Artificial Intelligence and Computer Science	P	1
BPOI1_2016	Computer and Information Science	P	1
BPOI_BO_2016	Common courses	P	1
BPOI4_2016	Computer Games and Graphics	P	1
BPOI3_2016	Software	P	1
BPOI2_2016	Internet of Things	P	1
BPEEM1_2016	Applied Electrical Engineering	P	1
BPEEM_BO_2016	Common courses	P	1
BPEEM2_2016	Electrical Engineering and Management	P	1
BPKYR_2021	Common courses	P	1
BPEK_2016	Common courses	P	1
BPKYR_2016	Common courses	P	1

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Page updated 21.11.2024 12:51:42, semester: L/2023-4, Z,L/2024-5, Z/2025-6, Send comments about the content to the Administrators of the Academic Programs

Proposal and Realization: I. Halaška (K336), J. Novák (K336)