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) 


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. GrammSchmidt 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

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  or  UMB/CV551  or  UMB/010  or  UMB/551 
Assessment methods and criteria 
Combined exam, Interim evaluation

Recommended literature 

Study plans that include the course 
Faculty  Study plan (Version)  Category of Branch/Specialization  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 