100222 Linear Algebra II

Course offering details

Instructors: Dr. Pavel Tumarkin

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
  • Further linear algebra
  • 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 Mon, 1. Feb. 2010 11:15 12:30 East Hall 3 Dr. Pavel Tumarkin
2 Mon, 8. Feb. 2010 11:15 12:30 East Hall 3 Dr. Pavel Tumarkin
3 Mon, 15. Feb. 2010 11:15 12:30 East Hall 3 Dr. Pavel Tumarkin
4 Th, 18. Feb. 2010 11:15 12:30 East Hall 3 Dr. Pavel Tumarkin
5 Th, 18. Feb. 2010 11:15 12:30 East Hall 3 Dr. Pavel Tumarkin
6 Mon, 22. Feb. 2010 11:15 12:30 East Hall 3 Dr. Pavel Tumarkin
7 Th, 25. Feb. 2010 11:15 12:30 East Hall 3 Dr. Pavel Tumarkin
8 Th, 25. Feb. 2010 11:15 12:30 East Hall 3 Dr. Pavel Tumarkin
9 Mon, 1. Mar. 2010 11:15 12:30 East Hall 3 Dr. Pavel Tumarkin
10 Th, 4. Mar. 2010 11:15 12:30 East Hall 3 Dr. Pavel Tumarkin
11 Mon, 8. Mar. 2010 11:15 12:30 East Hall 3 Dr. Pavel Tumarkin
12 Th, 11. Mar. 2010 11:15 12:30 East Hall 3 Dr. Pavel Tumarkin
13 Mon, 15. Mar. 2010 11:15 12:30 East Hall 3 Dr. Pavel Tumarkin
14 Th, 18. Mar. 2010 11:15 12:30 East Hall 3 Dr. Pavel Tumarkin
15 Mon, 22. Mar. 2010 11:15 12:30 East Hall 3 Dr. Pavel Tumarkin
16 Th, 25. Mar. 2010 11:15 12:30 East Hall 3 Dr. Pavel Tumarkin
17 Th, 8. Apr. 2010 11:15 12:30 East Hall 3 Dr. Pavel Tumarkin
18 Mon, 12. Apr. 2010 11:15 12:30 East Hall 3 Dr. Pavel Tumarkin
19 Th, 15. Apr. 2010 11:15 12:30 East Hall 3 Dr. Pavel Tumarkin
20 Mon, 19. Apr. 2010 11:15 12:30 East Hall 3 Dr. Pavel Tumarkin
21 Th, 22. Apr. 2010 11:15 12:30 East Hall 3 Dr. Pavel Tumarkin
22 Mon, 26. Apr. 2010 11:15 12:30 East Hall 3 Dr. Pavel Tumarkin
23 Th, 29. Apr. 2010 11:15 12:30 East Hall 3 Dr. Pavel Tumarkin
24 Mon, 3. May 2010 11:15 12:30 East Hall 3 Dr. Pavel Tumarkin
25 Th, 6. May 2010 11:15 12:30 East Hall 3 Dr. Pavel Tumarkin
26 Mon, 10. May 2010 11:15 12:30 East Hall 3 Dr. Pavel Tumarkin
27 Th, 20. May 2010 16:00 18:00 East Hall 3 Dr. Pavel Tumarkin
Course specific exams
Description Date Instructors Mandatory
1. Final Grade No Date Yes
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
Dr. Pavel Tumarkin