A
vector space (also called a
linear space) is a collection of objects called
vectors, which may be
added together and
multiplied ("scaled") by numbers, called
scalars in this context. Scalars are often taken to be
real numbers, but there are also vector spaces with scalar multiplication by
complex numbers,
rational numbers, or generally any
field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called
axioms, listed below.