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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