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Math Help - Space and dimension

  1. #1
    MHF Contributor Also sprach Zarathustra's Avatar
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    Space and dimension

    Let V be vector space with dimension of  n above C (complex plane). Now we look at him (V) like vector space above R. What his dimension above R?
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  2. #2
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    Try constructing \mathbb{C} (the complex plane) as a vector field using elements of \mathbb{R}.

    Conclude the relation between them from the above.
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  3. #3
    MHF Contributor Also sprach Zarathustra's Avatar
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    So the dimension is 2n or I missing something...?
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    help...
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  5. #5
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    Quote Originally Posted by Also sprach Zarathustra View Post
    So the dimension is 2n or I missing something...?
    Yes, since we can "construct" every element in \mathbb{C} using 2 elements of \mathbb{R}, we may conclude that the dimension of a vector space spanned over \mathbb{R} is twice than of the vector space spanned over \mathbb{C}.
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