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 Definition:

 Axioms:

 Addition Commutes:

 Addition Associates:

 Scalar Multiplication Distributes:

 Unique Zero Element:

 Field Unit Element:

 Span:

 Suppose .
 spans iff
any
can be written as .
 This is written .
 is a
linear combination of the vectors in .
 Basis:

 Any minimal spanning set is a basis.
 All bases are the same size.
 Dimension:

 The number of vectors in any basis.
 We will work in 2 and 3 dimensional spaces.
 Note:
 In the definition of a Vector Space:
 No notion of distance or size
 No notion of angles
 No ``points''
These are Euclidean and Affine space concepts.
CS488/688: Introduction to Interactive Computer Graphics
University of Waterloo
Computer Graphics Lab
cs488@cgl.uwaterloo.ca