M2110 Linear Algebra and Geometry II

Faculty of Science
Spring 2016
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Recommended Type of Completion: zk (examination). Other types of completion: z (credit).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
doc. RNDr. Jiří Kaďourek, CSc. (seminar tutor)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 8:00–9:50 A,01026
  • Timetable of Seminar Groups:
M2110/01: Thu 15:00–16:50 M4,01024, M. Čadek
M2110/02: Thu 12:00–13:50 M4,01024, M. Čadek
M2110/04: Wed 14:00–15:50 M2,01021, J. Kaďourek
Prerequisites
M1110 Linear Algebra I || M1111 Linear Algebra I ||( FI:MB003 Linear Algebra and Geometry I )
Knowledege of basic notion of linear algebra is supposed.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Abstract
The aim of this second course in linear algebra is to introduce other basic notions of linear algebra. Passing the course the students *will know affine spaces, bilinear and quadratic forms, eingenvalues and eigenvectors of linear operators, *they will be able to solve problems concerning the spaces with scalar product and properties of orthogonal and selfadjoint operators and *to find the Jordan canonical form.
Key topics
Affine geometry: affine spaces and subspaces, affine geometry and affine mappings. Linear forms: dual space, dual basis, dual homomorphism. Bilinear and quadratic forms: definition, matrix with respect to given basis, diagonalization, signature. Euklidean geometry: orthogonal projection, distance and deviation of affine subspaces. Linear operators: invariant subspaces, eigenvalues and eigen vectors, charakteristic polynomial, algebraic and geometric multiplicity of eigenvalues, conditions for diagonalization. Ortogonal and unitar operators: definition and basic properties, eigenvalues, geometric meaning. Self adjoint operators: adjoint operator, symmetric and hermitian matrices, spectral decomposition. Jordan canonical form: nilpotent endomorphisms, root subspaces, computations.
Study resources and literature
  • Zlatoš P.: Lineárna algebra a geometria, připravovaná skripta MFF Univerzity Komenského v Bratislavě, elektronicky dostupné na http://www.math.muni.cz/pub/math/people/Paseka/lectures/LA/
  • Slovák, Jan. Lineární algebra. Učební texty. Brno:~Masarykova univerzita, 1998. 138. elektronicky dostupné na http://www.math.muni.cz/~slovak.
Approaches, practices, and methods used in teaching
Lectures and exercises (tutorials).
Method of verifying learning outcomes and course completion requirements
Exam: written and oral. Requirements for the exam: to obtain 50% of points from tests written during semester. Requirements: to manage the theory from the lecture, to be able to solve the problems similar to those from exercises
Language of instruction
Czech
Follow-Up Courses
Teacher's information
http://www.math.muni.cz/~cadek
Písemná zkouška má část početní a teoretickou. Studenti, kteří z každé časti získají předepsaný bodů, postupují k ústní zkoušce. Při ní bude vyžadováno porozumění předneseným tématům a schopnost demonstrovat vyložené pojmy a věty na příkladech. Ke zkoušce je potřeba získat zápočet ze cvičení. Cvičící budou na každém cvičení zadávat domácí úlohy. Na začátku následujícího cvičení se bude psát krátká písemka (maximálně 15 minut). Její zadání bude velice blízké zadání některého příkladu z domácí úlohy. Těchto písemek bude celkem 8, za každou se budou udělovat maximálně 2 body. Každý student by měl v součtu získat aspoń 8 bodů (z celkového počtu 16) na udělení zápočtu.
Further comments (probably available only in Czech)
Study Materials
Information on completion of the course: ukončení zápočtem možné pouze rozhodnutím učitele
The course is taught annually.
Credit evaluation note: 2 kr. zápočet.
Listed among pre-requisites of other courses
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2000, Spring 2001, Spring 2002, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025, Spring 2026, Spring 2027.
  • Enrolment Statistics (Spring 2016, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2016/M2110