Linear Algebra 2

Lecturers:

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. Probelm class Fridays 4-5 in SM2 (following a 10 min break after the lecture, will hopefully move both to the same SM).



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 5pm Thursday 21st March       Solutions     Questions 4-6 of Exercise Sheet 6.

Assignment 8 Due       Solutions
Assignment 9 Due       Solutions



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.)
In Section 3.4, in line3 3,6 of that Section: (v-I) should be (f-I).


In Appendix 1 Page 1, 4th and 6th line under Proof: (-1)j-1 should be (-1)i-1.
Page 2, formula (0.4) the very last subscript should (i)+1 should be (i+1).


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



EXAM REVISION MATERIAL

Will appear below.