Vector Spaces
Vectors are actually more simple than points. So we will start our discussion with them.
Vectors are entities that live in a vector space.
A vector space is any set of elements that satisfies the following rules.
- The operations of addition and scalar multiplication must be defined, and
the set must be closed under them:
- Associativity of addition must hold:
- There exists a zero vector in V, denoted as
 , such that:
- For every element in V there exists an additive inverse:
- Scalar multiplication distributes over addition:
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