(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let {e_{1},...,e^{n}} be a basis for a complex vector space X. Find a basis for X regarded as a real vector space. What is the dimension of X in either case?

2. Relevant equations

3. The attempt at a solution

I'm really not sure where to begin with this question.

Are the e_{j}'s something like (i, 0, 0,...), (0,i,0,...)?

If so, could we take {ie_{1},....,ie_{n}} as the basis for X regarded as a real vector space?

Also, I think that the dimension in either case is n. Does anyone know if that is correct?

Thank you very much.

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# Basis - Complex Vector Space and Real Vector Space

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