100221 Linear Algebra I

Course offering details

Instructors: Dr. Stefan Maubach

Type: Lecture

Org-unit:

Course Name Abbreviation: LinAlg I

Hours per week: 3

Credits: 7.50

Min. | Max. participants: - | -

Partial Grades:
Final Grade

Official Course Description:
Together with 100211 Analysis I, this is one of the basic mathematics courses. It introduces vector spaces and linear maps, which play an important role throughout mathematics and its applications.
The course begins by introducing the concept of a vector space over an arbitrary field (for example, the real or complex numbers) and the concept of linear independence, leading to the notion of ``dimension''. We proceed to define linear maps between vector spaces and discuss properties such as nullity and rank. Linear maps can be represented by matrices and we show how matrices can be used to compute ranks and kernels of linear maps or to solve linear systems of equations.
In order to study some geometric problems and talk about lengths and angles, we introduce an additional structure called the inner or scalar product on real vector spaces. Properties of Euclidean vector spaces and orthogonal maps are treated, including the Cauchy-Schwarz inequality, Gram-Schmidt orthonormalization and orthogonal and unitary groups.
An endomorphism is a linear map from a vector space to itself and is represented by a square matrix. We study the trace and determinant of endomorphisms and matrices and discuss eigenvalues and eigenvectors. We discuss the question whether a matrix is diagonalizable and state the theorem on Jordan Normal Form which provides a classification of endomorphisms.
This course has no formal prerequisites; incoming students with a strong mathematics background are encouraged to take this class in their first semester. However, a familiarity with mathematical reasoning and proof (e.g., proof by induction or by contradiction), such as introduced in 110100 General Mathematics and Computational Science, is required.

Literature
Primary Text
  • Linear Algebra and Geometry
Required Reading (To view a list click a category.)
Recommended Reading (To view a list click a category.)
Appointments
Date From To Room Instructors
1 Wed, 4. Sep. 2013 09:45 11:00 East Hall 4 Dr. Stefan Maubach
2 Mon, 9. Sep. 2013 08:15 09:30 East Hall 4 Dr. Stefan Maubach
3 Wed, 11. Sep. 2013 09:45 11:00 East Hall 4 Dr. Stefan Maubach
4 Mon, 16. Sep. 2013 08:15 09:30 East Hall 4 Dr. Stefan Maubach
5 Wed, 18. Sep. 2013 09:45 11:00 East Hall 4 Dr. Stefan Maubach
6 Mon, 23. Sep. 2013 08:15 09:30 East Hall 4 Dr. Stefan Maubach
7 Wed, 25. Sep. 2013 09:45 11:00 East Hall 4 Dr. Stefan Maubach
8 Mon, 30. Sep. 2013 08:15 09:30 East Hall 4 Dr. Stefan Maubach
9 Wed, 2. Oct. 2013 09:45 11:00 East Hall 4 Dr. Stefan Maubach
10 Mon, 7. Oct. 2013 08:15 09:30 East Hall 4 Dr. Stefan Maubach
11 Wed, 9. Oct. 2013 09:45 11:00 East Hall 4 Dr. Stefan Maubach
12 Mon, 14. Oct. 2013 08:15 09:30 East Hall 4 Dr. Stefan Maubach
13 Wed, 16. Oct. 2013 09:45 11:00 East Hall 4 Dr. Stefan Maubach
14 Wed, 23. Oct. 2013 09:45 11:00 East Hall 4 Dr. Stefan Maubach
15 Mon, 28. Oct. 2013 08:15 09:30 East Hall 4 Dr. Stefan Maubach
16 Wed, 30. Oct. 2013 09:45 11:00 East Hall 4 Dr. Stefan Maubach
17 Mon, 4. Nov. 2013 08:15 09:30 East Hall 4 Dr. Stefan Maubach
18 Wed, 6. Nov. 2013 09:45 11:00 East Hall 4 Dr. Stefan Maubach
19 Mon, 11. Nov. 2013 08:15 09:30 East Hall 4 Dr. Stefan Maubach
20 Wed, 13. Nov. 2013 09:45 11:00 East Hall 4 Dr. Stefan Maubach
21 Mon, 18. Nov. 2013 08:15 09:30 East Hall 4 Dr. Stefan Maubach
22 Wed, 20. Nov. 2013 09:45 11:00 East Hall 4 Dr. Stefan Maubach
23 Mon, 25. Nov. 2013 08:15 09:30 East Hall 4 Dr. Stefan Maubach
24 Wed, 27. Nov. 2013 09:45 11:00 East Hall 4 Dr. Stefan Maubach
25 Mon, 2. Dec. 2013 08:15 09:30 East Hall 4 Dr. Stefan Maubach
26 Wed, 4. Dec. 2013 09:45 11:00 East Hall 4 Dr. Stefan Maubach
27 Wed, 18. Dec. 2013 12:30 14:30 Lecture Hall Research III Dr. Stefan Maubach
Course specific exams
Description Date Instructors Mandatory
1. Final Grade No Date No
2. Final Grade No Date No
Contained in course catalogues
Course catalogue
Course Catalogue > School of Engineering and Science > Mathematical Sciences > Undergraduate Level Courses
Class Session Overview
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Instructors
Dr. Stefan Maubach