100221 Linear Algebra I

Course offering details

Instructors: Prof. Dr. Ivan B. Penkov

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.

Additional Information:
All participants are strongly encouraged to fill in the teaching evaluation.

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 Fri, 3. Sep. 2010 08:15 09:30 East Hall 4 Prof. Dr. Ivan B. Penkov
2 Wed, 8. Sep. 2010 11:15 12:30 East Hall 4 Prof. Dr. Ivan B. Penkov
3 Fri, 10. Sep. 2010 08:15 09:30 East Hall 4 Prof. Dr. Ivan B. Penkov
4 Wed, 15. Sep. 2010 11:15 12:30 East Hall 4 Prof. Dr. Ivan B. Penkov
5 Fri, 17. Sep. 2010 08:15 09:30 East Hall 4 Prof. Dr. Ivan B. Penkov
6 Wed, 22. Sep. 2010 11:15 12:30 East Hall 4 Prof. Dr. Ivan B. Penkov
7 Fri, 24. Sep. 2010 08:15 09:30 East Hall 4 Prof. Dr. Ivan B. Penkov
8 Wed, 29. Sep. 2010 11:15 12:30 East Hall 4 Prof. Dr. Ivan B. Penkov
9 Fri, 1. Oct. 2010 08:15 09:30 East Hall 4 Prof. Dr. Ivan B. Penkov
10 Wed, 6. Oct. 2010 11:15 12:30 East Hall 4 Prof. Dr. Ivan B. Penkov
11 Fri, 8. Oct. 2010 08:15 09:30 East Hall 4 Prof. Dr. Ivan B. Penkov
12 Wed, 13. Oct. 2010 11:15 12:30 East Hall 4 Prof. Dr. Ivan B. Penkov
13 Fri, 15. Oct. 2010 08:15 09:30 East Hall 4 Prof. Dr. Ivan B. Penkov
14 Wed, 20. Oct. 2010 11:15 12:30 East Hall 4 Prof. Dr. Ivan B. Penkov
15 Fri, 22. Oct. 2010 08:15 09:30 East Hall 4 Prof. Dr. Ivan B. Penkov
16 Wed, 27. Oct. 2010 11:15 12:30 East Hall 4 Prof. Dr. Ivan B. Penkov
17 Fri, 29. Oct. 2010 08:15 09:30 East Hall 4 Prof. Dr. Ivan B. Penkov
18 Wed, 3. Nov. 2010 11:15 12:30 East Hall 4 Prof. Dr. Ivan B. Penkov
19 Fri, 5. Nov. 2010 08:15 09:30 East Hall 4 Prof. Dr. Ivan B. Penkov
20 Wed, 10. Nov. 2010 11:15 12:30 East Hall 4 Prof. Dr. Ivan B. Penkov
21 Fri, 12. Nov. 2010 08:15 09:30 East Hall 4 Prof. Dr. Ivan B. Penkov
22 Wed, 17. Nov. 2010 11:15 12:30 East Hall 4 Prof. Dr. Ivan B. Penkov
23 Fri, 19. Nov. 2010 08:15 09:30 East Hall 4 Prof. Dr. Ivan B. Penkov
24 Wed, 24. Nov. 2010 11:15 12:30 East Hall 4 Prof. Dr. Ivan B. Penkov
25 Fri, 26. Nov. 2010 08:15 09:30 East Hall 4 Prof. Dr. Ivan B. Penkov
26 Wed, 1. Dec. 2010 11:15 12:30 East Hall 4 Prof. Dr. Ivan B. Penkov
27 Fri, 3. Dec. 2010 08:15 09:30 East Hall 4 Prof. Dr. Ivan B. Penkov
28 Th, 16. Dec. 2010 16:00 18:00 East Hall 4 Prof. Dr. Ivan B. Penkov
Course specific exams
Description Date Instructors Mandatory
1. Final Grade No Date No
Contained in course catalogues
Course catalogue
Course Catalogue > School of Engineering and Science > Undergraduate Programs > Mathematics
Class Session Overview
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Instructors
Prof. Dr. Ivan B. Penkov