vector space

vector space
a) A type of set of vectors that satisfies a specific group of constraints.

A vector space is a set of vectors which can be linearly combined.

b) 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.

Each vector space has a basis and dimension. vector space over the field F

Syn: linear space

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