Math 2406: Abstract Vector Spaces

Lecture 4 Plan  (Thursday, August 30, 2007).

Apostol 1.14-1.16, 3.1-3.4.

We will go through some of topics from last time that we didn't get to. We will also skip Chapter 2, which is something of a detour into geometry. We may come back to it later if time permits. We are instead going to begin Chapter 3, which starts with the axiomatic definition of linear spaces.  So far in Chapter 1 we've studied a special case of a linear space: a linear space of vectors. Chapter 3 deals with linear spaces in general.

Review questions:

1. How is "basis" an appropriate name?
2. Why is "closure" used to describe the Closure Axioms?
3. In the examples of section 3.3 which are not linear spaces, which axioms are most commonly violated?

Homework 2 due Thursday, September 6, 2007 at 5 p.m. in Skiles 238A door box.

1. Apostol 1.15, Exercise 15.

2. Apostol 1.15, Exercise 20.

3. Apostol 1.17, Exercise 3.

4. Apostol 3.5, Exercise 2.

5. Apostol 3.5, Exercise 10 (see Exercise 9 for the definition of rational function).