Faculty of Electrical Engineering

Czech Technical University in Prague

CTU in Prague

Subject description - A0B01LAA

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A0B01LAA Linear Algebra and its Applications Extent of teaching:3+3
Guarantors:  Roles:P,V Language of
teaching:
CS
Teachers:Velebil J. Completion:Z,ZK
Responsible Department:13101 Credits:8 Semester:Z

Anotation:

The course covers standard basics of matrix calculus (determinants, inverse matrix) and linear algebra (linear space,basis, dimension, euclidean spaces, linear transformations) including eigenvalues and eigenvectors. Notions are illustrated in applications: matrices are used when solving systems of linear equations, eigenvalues are used for solving systems of linear differential equations.

Course outlines:

1. Systems of linear equations. Gauss elimination method.
2. Linear spaces, linear dependence and independence.
3. Basis, dimension, coordinates of vectors.
4. Rank of a matrix, the Frobenius theorem.
5. Linear mappings. Matrix of a linear mapping.
6. Matrix multiplication, inverse matrix. Determinants.
7. Inner product.Expanding vector w.r.t. orthonormal basis. Fourier basis.
8. Eigenvalues and eigenvectors of matrices and linear mappings.
9. Differential equations. Method of separation of variables.
10. Linear differential equations, homogeneous and non-homogeneous. Variation of parameter.
11. Linear differential equations with constant coefficients. Basis of solutions. Solving
non-homogeneous differential equations.
12. Systems of linear differential equations with constant coefficients. Basis of solutions.Solving non-homogeneous systems.
13. Applications. Numerical aspects.

Exercises outline:

1. Systems of linear equations. Gauss elimination method.
2. Linear spaces, linear dependence and independence.
3. Basis, dimension, coordinates of vectors.
4. Rank of a matrix, the Frobenius theorem.
5. Linear mappings. Matrix of a linear mapping.
6. Matrix multiplication, inverse matrix. Determinants.
7. Inner product.Expanding vector w.r.t. orthonormal basis. Fourier basis.
8. Eigenvalues and eigenvectors of matrices and linear mappings.
9. Differential equations. Method of separation of variables.
10. Linear differential equations, homogeneous and non-homogeneous. Variation of parameter.
11. Linear differential equations with constant coefficients. Basis of solutions. Solving
non-homogeneous differential equations.
12. Systems of linear differential equations with constant coefficients. Basis of solutions.Solving non-homogeneous systems.
13. Applications. Numerical aspects.

Literature:

1. P. Pták: Introduction to Linear Algebra. ČVUT, Praha, 2005.
2. P. Pták: Introduction to Linear Algebra. ČVUT, Praha, 1997. ftp://math.feld.cvut.cz/pub/krajnik/vyuka/ua/linalgeb.pdf

Requirements:

In order to obtain the certificate of attendance, students are required to actively participate in the laboratory class, hand in the assigned homework and obtain a sufficient score during lab tests. Only students who obtain attendance certificate ("zapocet") are allowed to take the exam. http://math.feld.cvut.cz/vivi/AE0B01LAA2010.pdf

Webpage:

http://math.feld.cvut.cz/velebil/teaching/a0b01laa.html

Subject is included into these academic programs:

Program Branch Role Recommended semester
BPKME2 Multimedia Technology P 1
BPKME4 Network and Information Technology P 1
BPKME5 Komunikace a elektronika P 1
BPKME3 Applied Electronics P 1
BPKME_BO Common courses P 1
BPKME1 Communication Technology P 1
BPOI_BO Common courses V 1
BPOI3 Software Systems V 1
BPOI2 Computer and Information Science V 1
BPOI1 Computer Systems V 1
BPEEM2 Electrical Engineering and Management P 1
BPEEM_BO Common courses P 1
BPEEM1 Applied Electrical Engineering P 1
BKSIT Common courses V 1
BPSTMIS Intelligent Systems V 1
BPSTMMI Manager Informatics V 1
BPSTMWM Web and Multimedia V 1
BPSIT Common courses V 1
BPSTM_BO Common courses V 1
BPSTMSI Software Engineering V 1
BSI(ECTS) Software Engineering V 1
BIS(ECTS) Intelligent Systems V 1
BWM(ECTS) Web and Multimedia V 1
BMI(ECTS) Manager Informatics V 1


Page updated 26.4.2018 14:49:04, semester: L/2018-9, Z,L/2017-8, Z/2018-9, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)
Responsible person: doc. Ing. Jiří Jakovenko, Ph.D.