Vector space
A set over or with operations of vector addition and scalar multiplication such that is an Abelian group and scalar multiplication distributes over addition, associates, and has identity .
Examples
In , vector addition composes position vectors along the parallelogram spanned by and , and for lies on the line with length . In both operations act componentwise:
The same componentwise definitions make a vector space over ; restricting scalars to , it is a real vector space of dimension .
Related
Stated in
- Definition 2.1 (Vector Space Over Reals and Complex Numbers)§2.1 Introduction on Vectors