# Vector Space

##### Updated: October 26, 2020

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