# 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.