Vector Space
A vector space $V$ over a field $F$ is a set of objects ( vectors), where two conditions hold.
- Firstly, vector addition of two vectors $\ket{a}, \ket{b} \in V$ will yield a third vector $\ket{a} + \ket{b} = \ket{c}$ , also contained in $V$ .
- The second condition is that scalar multiplication between some $\ket{a} \in V$ and some $n \in F$ , denoted by $n\ket{a}$ , is also contained within $V$ .