ABSTRACT
Geometrically, one can think of a vector as an object which has both a direction and a magnitude. The most basic setting for encountering vectors is in the real xy-plane, or in real xyz-space. The changing of magnitude via multiplication is called scalar multiplication, and the multipliers are called scalars. The main ingredients of a “vector space” seem to be existence of the two operations, are addition of the vectors and scalar multiplication of the vectors by elements of some field.
