Examples
The vector space R3 has
as a basis, and therefore we have dimR(R3) = 3. More generally, dimR(Rn) = n, and even more generally, dimF(Fn) = n for any field F.
The complex numbers C are both a real and complex vector space; we have dimR(C) = 2 and dimC(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.
Read more about this topic: Dimension (vector Space)
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