Course: Linear Algebra

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Course title Linear Algebra
Course code KMA/LA
Organizational form of instruction Lecture + Tutorial
Level of course Bachelor
Year of study 1
Semester Winter and summer
Number of ECTS credits 4
Language of instruction Czech
Status of course Compulsory, Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Čada Roman, Doc. Ing. Ph.D.
  • Ekstein Jan, RNDr. Ph.D.
  • Tomiczková Světlana, RNDr. Ph.D.
Course content
Week 1. Polynomials, Horner scheme, polynomial factorization Week 2. Vector space, linear dependence and independence, basis and dimension of a vector space, coordinates of a vector relative to a basis Week 3. Determinant of a matrix, definition and basic properties, determinant expansion along a row or a column Week 4. rank of a matrix, Gaussian elimination, calculation of the rank using determinants Week 5. matrix inverse, Gauss-Jordan elimination, calculation of the matrix inverse using determinants Week 6. linear map (transformation), kernel and image and their dimensions, associated matrix of a linear map and its properties Week 7. inverse linear map, linear map composition and associated matrix, vector space isomorphism, change of basis and change-of-basis matrix Week 8. systems of linear equations, homogeneous and non-homogeneous systems of equations, linear systems with an invertible matrix coefficient, Cramer's rule Week 9. eigenvalues and eigenvectors of a matrix, similarity of matrices and its properties, Jordan normal form of a matrix Week 10. inner product and its properties, norm induced by the inner product, orthogonal and orthonormal basis for a space Week 11. the Gram-Schmidt process, orthogonal projection of a vector on a subspace Week 12. method of least squares, quadratic forms and real valued symmetric matrices Week 13. inertia of a quadratic form, Sylvester's law of inertia for quadratic forms

Learning activities and teaching methods
Interactive lecture, Lecture with practical applications, Collaborative instruction
  • Contact hours - 52 hours per semester
  • Preparation for an examination (30-60) - 48 hours per semester
  • Preparation for formative assessments (2-20) - 10 hours per semester
prerequisite
professional knowledge
Knowledge of secondary school mathematics required.
learning outcomes
After completing the course the student will be able to - find roots of several types of polynomials, - use the concept of a vector and a matrix, - calculate the determinant of a square matrix and to find its inverse, - solve algebraic systems of linear equations, - define and verify a vector space structure, - work with the concept of a linear map, - find eigenvalues and eigenvectors of a square matrix and to interpret them geometrically, - classify quadric surfaces, - approximate functions (data) by the method of least squares.
teaching methods
Interactive lecture
Collaborative instruction
Lecture with practical applications
assessment methods
Combined exam
Test
Skills demonstration during practicum
Recommended literature
  • Havel, Václav; Holenda, Jiří. Lineární algebra. 1. vyd. Praha : SNTL, 1984.
  • Holenda, Jiří. Lineární algebra. 2. vyd. Plzeň : Západočeská univerzita, 1992. ISBN 80-7082-075-6.
  • Tesková, Libuše. Lineární algebra. 1. vyd. Plzeň : Západočeská univerzita, 2001. ISBN 80-7082-797-1.
  • Tesková, Libuše. Sbírka příkladů z lineární algebry. 5. vyd. Plzeň : Západočeská univerzita, 2003. ISBN 80-7043-263-2.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Applied Sciences Financial Informatics and Statistics (1) Economy 1 Winter
Faculty of Applied Sciences Building Structures (2010) Construction industry, geodesy and cartography 1 Winter
Faculty of Applied Sciences Geomatics (2012) Construction industry, geodesy and cartography 1 Winter
Faculty of Applied Sciences Geomatics (2015) Construction industry, geodesy and cartography 1 Winter
Faculty of Applied Sciences General Mathematics (2012) Mathematics courses 1 Winter
Faculty of Applied Sciences Information Systems (2015) Informatics courses 1 Winter
Faculty of Applied Sciences Computer Control of Systems and Processes (2012) Special and interdisciplinary fields 1 Winter
Faculty of Applied Sciences Computer Modelling (2014) Special and interdisciplinary fields 1 Winter
Faculty of Applied Sciences Information Technologies (2012) Informatics courses 1 Winter
Faculty of Applied Sciences Mathematics and its Applications (2015) Mathematics courses 1 Winter
Faculty of Applied Sciences Geomatics (2014) Construction industry, geodesy and cartography 1 Winter
Faculty of Applied Sciences Geomatics (2014) Construction industry, geodesy and cartography 1 Winter
Faculty of Applied Sciences Mathematics and its Applications (2015) Mathematics courses 1 Winter
Faculty of Applied Sciences Systems for Identification, Security and Communication (2012) Special and interdisciplinary fields 1 Winter
Faculty of Applied Sciences Building Structures (2013) Construction industry, geodesy and cartography 1 Winter
Faculty of Applied Sciences Land-use Planning (2014) Special and interdisciplinary fields 1 Winter
Faculty of Applied Sciences Computer Systems (2012) Electrical engineering, telecommunication and IT 1 Winter
Faculty of Applied Sciences Information Technologies (2013) Informatics courses 1 Winter
Faculty of Applied Sciences General Mathematics (2012) Mathematics courses 1 Winter
Faculty of Applied Sciences Mathematics and Management (2011) Mathematics courses 1 Winter
Faculty of Applied Sciences Computations and Design (1) Special and interdisciplinary fields 1 Winter
Faculty of Applied Sciences Land-use Planning (2013) Special and interdisciplinary fields 1 Winter
Faculty of Applied Sciences Information Systems (2012) Informatics courses 1 Winter
Faculty of Applied Sciences Cybernetics and Control Engineering (2012) Special and interdisciplinary fields 1 Winter
Faculty of Applied Sciences Financial Informatics and Statistics (2007) Economy 1 Winter
Faculty of Applied Sciences Mathematics for Science (2012) Mathematics courses 1 Winter
Faculty of Applied Sciences Mathematics for Business Studies (2015) Mathematics courses 1 Winter
Faculty of Applied Sciences Scientific Computing and Modelling (2011) Mathematics courses 1 Winter
Faculty of Applied Sciences Computer Control of Systems and Processes (2015) Special and interdisciplinary fields 1 Winter
Faculty of Applied Sciences Systems for Identification, Security and Communication (2015) Special and interdisciplinary fields 1 Winter
Faculty of Applied Sciences Cybernetics and Control Engineering (2013) Special and interdisciplinary fields 1 Winter
Faculty of Applied Sciences Computer Systems (2013) Electrical engineering, telecommunication and IT 1 Winter
Faculty of Applied Sciences Information Systems (2014) Informatics courses 1 Winter
Faculty of Applied Sciences Information Systems (1) Informatics courses 1 Winter
Faculty of Applied Sciences Information Technologies (2015) Informatics courses 1 Winter
Faculty of Applied Sciences Mathematics for Business Studies (2011) Mathematics courses 1 Winter
Faculty of Applied Sciences Intelligent Man-Machine Communication (2012) Special and interdisciplinary fields 1 Winter
Faculty of Applied Sciences Computations and Design (2014) Special and interdisciplinary fields 1 Winter
Faculty of Applied Sciences Applied and Engineering Physics (2012) Special and interdisciplinary fields 1 Winter
Faculty of Applied Sciences Intelligent Man-Machine Communication (2015) Special and interdisciplinary fields 1 Winter