# l9 - Math 20F Linear Algebra Lecture 9 4.1 Vector Spaces...

This preview shows pages 1–2. Sign up to view the full content.

Math 20F Linear Algebra Lecture 9: 4.1 Vector Spaces. Recall that if x , y R n are vectors in Euclidean space we deﬁned the addition x + y R n and scalar multiplication λ x R n . In dimensions 2 and 3 we can deﬁne these notions geometrically The addition and scalar multiplication satisfy certain properties listed below, but these properties show up in many diﬀerent contexts so rather than studying each situation individually we will study them all at once. A set V with two operations, addition and multiplication by scalars, deﬁned on it is called a vector space if the following properties hold for any u , v , w V α,β R : 1. If u , v V then u + v V . (closure under addition) 2. u + v = v + u (commutative) 3. ( u + v ) + w ) = u + ( v + w ) (associative) 4. There is an element 0 V such that u + 0 = u all u V (additive unit) 5. For each u V there is - u V such that u + ( - u ) = 0 (additive inverse) 6. If u V and α is a scalar then α u V . (closure under scalar multiplication)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 04/29/2008 for the course MATH 20F taught by Professor Buss during the Spring '03 term at UCSD.

### Page1 / 2

l9 - Math 20F Linear Algebra Lecture 9 4.1 Vector Spaces...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online