Question

What is the dimensions of complex vector space over the field of complex number?

Answer 1

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.

Answer 2

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.

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