°A set
V, whose elements are called "vectors", together with a binary operation + forming a
module (
V,+), and a set
F* of
bilinear unary functions
f*:
V→
V, each of which corresponds to a "
scalar" element
f of a
field F, such that the composition of elements of
F* corresponds isomorphically to multiplication of elements of
F, and such that for any vector v, 1*(v) = v.
"Any field is a one-dimensional vector space over itself."
synonyms:
linear space