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$R/C$ represent real/complex respectively.

a) Explain why we can regard $V$ as a vector space $V_r$ over $R$.
b) Determine the dimension $d$ of $V_r$.
c) Find an isomorphism of $V_r$ with $R^d$.

I'm not really sure what this means. All real numbers, are complex numbers but not all complex numbers are real numbers, so I'm not sure how we can regard $V$ as a vector space over $R$. Surely it may have elements in $C$ that aren't also in $R$?

I think it has maybe something to do with: Complexification. Which means I also think the dimension $d$ of $V_r$ is $n$.

But how would I find an isomorphism either?

Stefan Hamcke
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Kurt
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1 Answers1

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Hint: $\{1,i\}$ is a basis for the real space $\mathbb C$.

Martin Argerami
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  • Unfortunately I didn't find this helped me, so I did some more searching, and after a while I stumbled upon this which did help me: http://math.stackexchange.com/questions/48510/how-to-prove-that-complex-numbers-c-are-linear-space-over-real-numbers-r-fie – Kurt Oct 28 '13 at 02:36