a vector is an element, commonly an ordered n-tuple, in a set, commonly an n-dimensional space, satisfying the properties of a vector space.
V is a vector space over the field F if:
it has two operations defined on it, vector addition, and scalar multiplication.
it satisfies the following properties:
associative addition of vectors
commutative addition of vectors
there is a "zero" vector satisfying additive identity
every vector has an additive inverse
distributivity of scalar multiplication, c(u+v) = cu + cv
distributivity of scalar multiplication, (c+d)u = cu + du
a(bv) = (ab)v for a,b in F, v in V
scalar multiplication has an identity element
V is necessarily closed under vector addition and scalar multiplication
also
>>11
>>13
fail.