100222 Linear Algebra II

Course offering details

Instructors: Dr. Ivan Ovsyannikov

Type: Lecture

Org-unit:

Course Name Abbreviation: LinAlg II

Hours per week: 3

Credits: 7.50

Min. | Max. participants: - | -

Partial Grades:
Final Grade

Official Course Description:
This course continues Analysis I and complements Analysis II. It continues
with the classification of matrices and introduces elements of tensor algebra.
In the first part, we continue the discussion of endomorphisms, discussing the Cayley-
Hamilton Theorem and minimal polynomials, and giving some versions of Jordan normal form
over non-algebraically closed fields.
The second part of the course deals with dual spaces and quadratic, symmetric and skewsymmetric
forms. We introduce the dual vector space and dual linear maps and their relation
with bilinear forms. Classifications are given of symmetric and skew-symmetric real bilinear
forms and of Hermitian and skew-Hermitian forms over the complex numbers.
The last part is concerned with tensors — objects that play an important role in many
branches of physics and mathematics. The tensor product of two (or more) vector spaces is
introduced and properties are discussed including the universal property, contraction of tensors,
‘outer’ and ‘inner’ products, and the relationship between linear maps and tensors.

Literature
Primary Text
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 Tue, 3. Feb. 2015 11:15 12:30 East Hall 4 Dr. Ivan Ovsyannikov
2 Th, 5. Feb. 2015 09:45 11:00 East Hall 4 Dr. Ivan Ovsyannikov
3 Tue, 10. Feb. 2015 11:15 12:30 East Hall 4 Dr. Ivan Ovsyannikov
4 Th, 12. Feb. 2015 09:45 11:00 East Hall 4 Dr. Ivan Ovsyannikov
5 Tue, 17. Feb. 2015 11:15 12:30 East Hall 4 Dr. Ivan Ovsyannikov
6 Th, 19. Feb. 2015 09:45 11:00 East Hall 4 Dr. Ivan Ovsyannikov
7 Tue, 24. Feb. 2015 11:15 12:30 East Hall 4 Dr. Ivan Ovsyannikov
8 Th, 26. Feb. 2015 09:45 11:00 East Hall 4 Dr. Ivan Ovsyannikov
9 Tue, 3. Mar. 2015 11:15 12:30 East Hall 4 Dr. Ivan Ovsyannikov
10 Th, 5. Mar. 2015 09:45 11:00 East Hall 4 Dr. Ivan Ovsyannikov
11 Tue, 10. Mar. 2015 11:15 12:30 East Hall 4 Dr. Ivan Ovsyannikov
12 Th, 12. Mar. 2015 09:45 11:00 East Hall 4 Dr. Ivan Ovsyannikov
13 Tue, 17. Mar. 2015 11:15 12:30 East Hall 4 Dr. Ivan Ovsyannikov
14 Th, 19. Mar. 2015 09:45 11:00 East Hall 4 Dr. Ivan Ovsyannikov
15 Tue, 24. Mar. 2015 11:15 12:30 East Hall 4 Dr. Ivan Ovsyannikov
16 Th, 26. Mar. 2015 09:45 11:00 East Hall 4 Dr. Ivan Ovsyannikov
17 Tue, 7. Apr. 2015 11:15 12:30 East Hall 4 Dr. Ivan Ovsyannikov
18 Th, 9. Apr. 2015 09:45 11:00 East Hall 4 Dr. Ivan Ovsyannikov
19 Tue, 14. Apr. 2015 11:15 12:30 East Hall 4 Dr. Ivan Ovsyannikov
20 Th, 16. Apr. 2015 09:45 11:00 East Hall 4 Dr. Ivan Ovsyannikov
21 Tue, 21. Apr. 2015 11:15 12:30 East Hall 4 Dr. Ivan Ovsyannikov
22 Th, 23. Apr. 2015 09:45 11:00 East Hall 4 Dr. Ivan Ovsyannikov
23 Tue, 28. Apr. 2015 11:15 12:30 East Hall 4 Dr. Ivan Ovsyannikov
24 Th, 30. Apr. 2015 09:45 11:00 East Hall 4 Dr. Ivan Ovsyannikov
25 Tue, 5. May 2015 11:15 12:30 East Hall 4 Dr. Ivan Ovsyannikov
26 Th, 7. May 2015 09:45 11:00 East Hall 4 Dr. Ivan Ovsyannikov
27 Tue, 12. May 2015 11:15 12:30 East Hall 4 Dr. Ivan Ovsyannikov
28 Wed, 20. May 2015 12:30 14:30 East Hall 4 Dr. Ivan Ovsyannikov
Course specific exams
Description Date Instructors Mandatory
1. Final Grade No Date No
Contained in course catalogues
Course catalogue
Course Catalogue > Engineering and Science > Mathematical Sciences > Undergraduate Level Courses
Class Session Overview
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Instructors
Dr. Ivan Ovsyannikov