Linear Algebra 2

Lecturers:

Dr. C. Harris (first 6 weeks of the course). Office and office hours: 1.4 Mathematics Building, Wednesday 1-2 or by appointment.
Dr. M. Rudnev (last 6 weeks of the course). Office and office hours: 2.10 Howard House, Thursday 1-2, 3-4 or by appointment.

Timetable: Lectures: Thursday 12-1 and 2-3 in SM1/SM2, respectively;
Friday 3-4 in SM1. Problem class Fridays 4-5 in SM1 also (following a 10 min break after the lecture).



Course description: LA 2 



HOMEWORK

To be handed in weekly and after having been marked collected from the two boxes (marked Linear Algebra 2 Homework for Marking, and Linear Algebra 2 Returned Homework) in the Main Building Lobby. Solutions will become accessible in due time.

Assignment 1 Due 5pm Thursday 7th February      Solutions

Assignment 2 Due 5pm Thursday 14th February    Solutions
Assignment 3 Due 5pm Thursday 21st February     Solutions
Assignment 4 Due 5pm Thursday 28th February    Solutions   Only do questions 1-5.
Assignment 5 Due 5pm Thursday 7th March          Solutions   Question 6 of Exercise Sheet 4 and Questions 1-4 of Exercise Sheet 5.
Assignment 6 Due 5pm Thursday 14th March       Solutions   Questions 5-6 of Exercise Sheet 5 and Questions 1-3 of Exercise Sheet 6.
Assignment 7 Due       Solutions 

Assignment 8 Due       Solutions
Assignment 9 Due       Solutions


PROBLEM CLASSES

Problem Classes every week on Friday 4pm (now in SM1).
Problem Class 1    with   Solutions

Problem Class 2    with   Solutions

Problem Class 3    with handwritten solutions available at the end of each problem class.

Problem Class 4    with handwritten solutions available at the end of each problem class.

Problem Class 5    with handwritten solutions available at the end of each problem class.



LECTURE NOTES

First set: Basics

Second set: Vector spaces
Third set: Matrices             Appendix 1: Proof of Cofactor theorem
Fourth set: Cayley-Hamilton and Jordan theorems         Appendix 2: Proof of Cayley-Hamilton theorem without quotient spaces
Fifth set: Bilinear forms and matrices       Appendix 3: More jargon-free statements and proofs of results on self-adjoint and orthogonal operators

ERRORS AND TYPOS IN NOTES (PLEASE HELP TO FIND MORE):

Second set:
In Def 2.1: needs to be added (4) a(u+v)=au+av, for any a in K and u,v in V.
In the first line of Section 2.1 replace subscript k by n (or replace n by k in the next line).
Example 2.38 in (3). Clarification: there are operators on vector spaces over K with no eigenvalues in the field K. (The eigenvalues will exist in the extension of K, its algebraic closure. Think of real matrices with complex eigenvalues.)


Third set:
Proposition 4.2 (2) should say deg pq ≤ deg p+deg q



EXAM REVISION MATERIAL

Will appear below.