F1110 Linear algebra and geometry

Faculty of Science
Autumn 2024
Extent and Intensity
2/2/0. 4 credit(s) (plus 2 credits for an exam). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Pavla Musilová, Ph.D. (lecturer)
Mgr. Pavla Musilová, Ph.D. (seminar tutor)
Kateřina Smetanová (assistant)
Guaranteed by
prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Timetable
Mon 14:00–15:50 F1 6/1014
  • Timetable of Seminar Groups:
F1110/01: Tue 8:00–9:50 F3,03015, P. Musilová
F1110/02: Tue 10:00–11:50 F3,03015, P. Musilová
F1110/03: Wed 8:00–9:50 F3,03015, P. Musilová
Prerequisites
Secondary school mathematics
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The first part of the fundamental course of linear and multilinear algebra and geometry for physicist. As the linear algebra and geometry are key mathematical tools for most physical theories, the aim of the discipline is to give students a sufficiently deep understanding of their concepts: Vector spaces and subspaces, linearity, linear mapping, practical calculus of matrices, and solving systems of linear equations.
Learning outcomes
Absolving the discipline students obtain following knowledge and practical skills:

* Understanding of the concept of a matrix and practical skills with calculus of matrices.
* Practical skills in solving systems of linear equations.
* Understanding of basic algebraic structures necessary for the concept of a vector space, understanding of the concept of vector space and subspace and the concept of linearity.
* Understanding of the theory of systems of linear equations in the context of vector spaces and subspaces.
Syllabus
  • 1. Matrices, calculus of matrices, rank of a matrix, Gauss elimination.
  • 2. Determinant of a matrix, inverse matrix.
  • 3. Solving systems of linear equations.
  • 4. Algebraic structures with one and two operations, groups, rings, fields.
  • 5. Vector spaces, linear dependent and linear independent systems of vectors.
  • 6. Base, dimension, transformations of bases.
  • 7. Vector subspaces.
  • 8. Vector subspaces generated by a system of vectors, intersection of vector spaces, complement.
  • 9. Examples of vector spaces and subspaces.
  • 10. Systems of linear equations and vector spaces.
  • 11. Linear mapping, vector spaces connected with a linear mapping.
  • 12. Representation of a linear mapping in bases, transformations of bases.
  • 13. Dual space, dual basis.
  • 14. Applications, examples.
Literature
    required literature
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika pro porozumění i praxi I (Mathematics for understanding and praxis I). Vydání druhé, doplněné. Brno: VUTIUM, VUT Brno, 2009, 339 pp. Vysokoškolské učebnice. ISBN 978-80-214-3631-2. info
    recommended literature
  • STRANG, Gilbert. Introduction to linear algebra. 4th ed. Wellesley, MA: Wellesley-Cambridge Press, 2009, ix, 574. ISBN 9780980232721. info
  • MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989, 281 s. info
    not specified
  • SLOVÁK, Jan. Lineární algebra. Učební texty. Brno: Masarykova univerzita, 1998, 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. info
Teaching methods
Lectures: theoretical explanation with practical examples
Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks, tests
Assessment methods
Teaching: lectures, exercises.
Exam: written test (consisting of two parts: (a) solving problems, (b) test), oral part. In the part (a) students demonstrate the ability of solving extensive and complex problems of linear algebra and geometry. In the part (b) they demonstrate the understanding of important concepts and theorems, as well as the good orientation in the discipline.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
The course is also listed under the following terms Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023.
  • Enrolment Statistics (recent)
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