dimK(V) = dimK(F) dimF(V). In particular, every complex vector space of dimension n is a real vector space of dimension 2n. Some simple formulae relate the dimension of a vector space with the cardinality of the base field and the cardinality of the space itself.
How do you describe vectors with N dimension?
We can generalize this concept to an arbitrary number of dimensions, say n dimensions. We refer to an n-dimensional vector as a vector in Rn and write it as an n-tuple of numbers: x=(x1,x2,x3,…,xn).
Is CN a vector space?
It is straightforward to show that Cn, together with the given operations of addition and scalar multiplication, is a complex vector space.
