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 (+)

$$\begin{equation} +\,:\,V\,\times\,V\,\longrightarrow\,V \end{equation}$$

• Multiplication ($\cdot$)

$$\begin{equation} \cdot\,:\,F\,\times\,V\,\longrightarrow\,V \end{equation}$$

where $F$ is any scalar