Vector space

A vec­tor space is a field \(F\) paired with a Group \(V\) and a func­tion \(\cdot : F \times V \to V\) (called “scalar mul­ti­pli­ca­tion”) such that \(1 \cdot v = v\) and such that scalar mul­ti­pli­ca­tion dis­tributes over ad­di­tion. Ele­ments of the field are called “scalars,” el­e­ments of the group are called “vec­tors.”

Also there are some nice ge­o­met­ric in­ter­pre­ta­tions and stuff.