Vector Space

also known as a linear space

A collection of objects known as “vectors”. In the Euclidean space these can be visualized as simple arrows with a direction and a length, but this analogy will not necessarily translate to all spaces.

Addition and multiplication of these objects (vectors) must adhere to a set of axioms for the set to be considered a “vector space”.

• Addition (+)

+:V×V⟶V

• Multiplication (⋅)

⋅:F×V⟶V

where F is any scalar