100222 Linear Algebra II

Course offering details

Instructors: Ph.D. Sergiy Vasylkevych

Type: Lecture

Org-unit:

Course Name Abbreviation: Lin Algebra II

Hours per week: 3

Credits: 7.50

Min. | Max. participants: - | -

Partial Grades:
Final Grade

Official Course Description:
This course continues 100211 Linear Algebra I and complements 100202 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 skew-symmetric 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
  • 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, 1. Feb. 2012 14:15 15:30 East Hall 8 Ph.D. Sergiy Vasylkevych
2 Mon, 6. Feb. 2012 11:15 12:30 East Hall 8 Ph.D. Sergiy Vasylkevych
3 Wed, 8. Feb. 2012 14:15 15:30 East Hall 8 Ph.D. Sergiy Vasylkevych
4 Mon, 13. Feb. 2012 11:15 12:30 East Hall 8 Ph.D. Sergiy Vasylkevych
5 Wed, 15. Feb. 2012 14:15 15:30 East Hall 8 Ph.D. Sergiy Vasylkevych
6 Mon, 20. Feb. 2012 11:15 12:30 East Hall 8 Ph.D. Sergiy Vasylkevych
7 Wed, 22. Feb. 2012 14:15 15:30 East Hall 8 Ph.D. Sergiy Vasylkevych
8 Mon, 27. Feb. 2012 11:15 12:30 East Hall 8 Ph.D. Sergiy Vasylkevych
9 Wed, 29. Feb. 2012 14:15 15:30 East Hall 8 Ph.D. Sergiy Vasylkevych
10 Mon, 5. Mar. 2012 11:15 12:30 East Hall 8 Ph.D. Sergiy Vasylkevych
11 Wed, 7. Mar. 2012 14:15 15:30 East Hall 8 Ph.D. Sergiy Vasylkevych
12 Mon, 12. Mar. 2012 11:15 12:30 East Hall 8 Ph.D. Sergiy Vasylkevych
13 Wed, 14. Mar. 2012 14:15 15:30 East Hall 8 Ph.D. Sergiy Vasylkevych
14 Mon, 19. Mar. 2012 11:15 12:30 East Hall 8 Ph.D. Sergiy Vasylkevych
15 Wed, 21. Mar. 2012 14:15 15:30 East Hall 8 Ph.D. Sergiy Vasylkevych
16 Mon, 26. Mar. 2012 11:15 12:30 East Hall 8 Ph.D. Sergiy Vasylkevych
17 Wed, 28. Mar. 2012 14:15 15:30 East Hall 8 Ph.D. Sergiy Vasylkevych
18 Wed, 11. Apr. 2012 14:15 15:30 East Hall 8 Ph.D. Sergiy Vasylkevych
19 Mon, 16. Apr. 2012 11:15 12:30 East Hall 8 Ph.D. Sergiy Vasylkevych
20 Wed, 18. Apr. 2012 14:15 15:30 East Hall 8 Ph.D. Sergiy Vasylkevych
21 Mon, 23. Apr. 2012 11:15 12:30 East Hall 8 Ph.D. Sergiy Vasylkevych
22 Wed, 25. Apr. 2012 14:15 15:30 East Hall 8 Ph.D. Sergiy Vasylkevych
23 Mon, 30. Apr. 2012 11:15 12:30 East Hall 8 Ph.D. Sergiy Vasylkevych
24 Wed, 2. May 2012 14:15 15:30 East Hall 8 Ph.D. Sergiy Vasylkevych
25 Mon, 7. May 2012 11:15 12:30 East Hall 8 Ph.D. Sergiy Vasylkevych
26 Wed, 9. May 2012 14:15 15:30 East Hall 8 Ph.D. Sergiy Vasylkevych
27 Mon, 14. May 2012 11:15 12:30 East Hall 8 Ph.D. Sergiy Vasylkevych
Course specific exams
Description Date Instructors Mandatory
1. Final Grade Th, 31. May 2012 12:30-14:30 Ph.D. Sergiy Vasylkevych No
Contained in course catalogues
Course catalogue
Course Catalogue > School of Engineering and Science > Undergraduate Programs > Mathematics
Class Session Overview
  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10
  • 11
  • 12
  • 13
  • 14
  • 15
  • 16
  • 17
  • 18
  • 19
  • 20
  • 21
  • 22
  • 23
  • 24
  • 25
  • 26
  • 27
Instructors
Ph.D. Sergiy Vasylkevych