Course: Linear Algebra II

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Course title Linear Algebra II
Course code UMB/585
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study not specified
Frequency of the course In each academic year, in the summer semester.
Semester Summer
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory
Form of instruction unspecified
Work placements unspecified
Recommended optional programme components None
Lecturer(s)
  • Zalabová Lenka, doc. Mgr. Ph.D.
Course content
The content of the course is the theory of (abstract) vector spaces. We study properties of vector spaces and linear objects defined on vector spaces. Content of lectures: Vector spaces and subspaces, linear (in)dependence of system of vectors, generating, basis, dimension. Intersection and sum of vector subspaces. Linear map and matrix of linear map in different basis, transizion matrix and transformation of coordinates. Linear forms. Bilinear and quadratic forms. Regulatiry, signature. Sylvester's law of inertia. Spaces with skalar product. Orthogonal/orthonormal systém of vectors. Gramm-Schmidt orthogonalization. Orthogonal projectors. Eigenvectors and eigenvalues of linear transformations. Jordan canonical form. Lectures of practicals: Application of linear algebra and geometry in examples.

Learning activities and teaching methods
Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Work with text (with textbook, with book), Individual preparation for exam
  • Preparation for classes - 56 hours per semester
  • Class attendance - 56 hours per semester
  • Preparation for exam - 56 hours per semester
Learning outcomes
The goal of the course is (abstract) linear algebra.
Student acquires basic subjects of linear algebra useful in mathematical analysis, geometry and numerical mathematics.
Prerequisites
Knowledge of matrix computations on the level of the course UMB551 Linear Algebra.
UMB/CV010
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UMB/CV551
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UMB/010
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UMB/551

Assessment methods and criteria
Combined exam, Interim evaluation

Recommended literature
  • BICAN, L. Lineární algebra. Praha, SNTL, 1979..
  • HALMOS, P.R. Finite-Dimensional Vector Spaces, Springer, 1974..
  • Lenka Zalabová. Skripta ke kurzu UMB585 Lineárni algebra II.
  • SLOVÁK, J. Lineární algebra. MU Brno, www.math.muni.cz/slovak/Vyuka/la.pdf..
  • ZLATOŠ, P. Lineární algebra. FMFI Bratislava, www.thales.doa.fmph.uniba.sk/katc/..


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Science Study plan (Version): Mathematics for future teachers (1) Category: Mathematics courses 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (1) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: Summer
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (1) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: Summer
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (1) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: Summer
Faculty: Faculty of Science Study plan (Version): Applied Mathematics (2010) Category: Mathematics courses 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Science Study plan (Version): Mathematics for future teachers (1) Category: Mathematics courses 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Science Study plan (Version): Mathematics for future teachers (1) Category: Mathematics courses 1 Recommended year of study:1, Recommended semester: Summer
Faculty: Faculty of Science Study plan (Version): Secondary Schools Teacher Training in Mathematics (2012) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: Summer
Faculty: Faculty of Science Study plan (Version): Mathematics for future teachers (1) Category: Mathematics courses 1 Recommended year of study:1, Recommended semester: Summer