.

In respect to this, are complex numbers a vector space?

With addition and scalar multiplication, the set of complex numbers forms a vector space of dimension 2 (where the scalars are the real numbers).

Likewise, is R 2 a vector space? To show that R2 is a vector space you must show that each of those is true. For example, if U= (a, b) and V= (c, d), where a, b, c, and d are real numbers, then U+ V= (a+ c, b+ d). Since addition of real numbers is "commutative", that is the same as (c+ a, d+ b)= (c, d)+ (a, b)= V+ U so (1), above, is true.

Just so, what is a real vector space?

A real vector space is a vector space whose field of scalars is the field of reals. A linear transformation between real vector spaces is given by a matrix with real entries (i.e., a real matrix). SEE ALSO: Complex Vector Space, Linear Transformation, Real Normed Algebra, Vector Basis, Vector Space.

What is the dimension of complex numbers?

The complex numbers C are both a real and complex vector space; we have dim_R(C) = 2 and dim_C(C) = 1. So the dimension depends on the base field. The only vector space with dimension 0 is {0}, the vector space consisting only of its zero element.