Vector space , dimension,

  • Thread starter ak123456
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1. The problem statement, all variables and given/known data
Let V be a vector space over C of dimenson n . We view V also as a vector space over R by restricting the scalar multiplication of C on V to R .Show that dimR(V) = 2n


2. Relevant equations



3. The attempt at a solution
I have to show that if x1,...xn form a basis of V over C then x1,....xn ix1,....ixn form a basis of V over R
but i still confuse about it
 

tiny-tim

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Hi ak123456! :smile:
I have to show that if x1,...xn form a basis of V over C then x1,....xn ix1,....ixn form a basis of V over R
That's right! :smile:

First prove that they are independent.

Then start with any element of V, and prove that it is a combination of them, with real coefficients :wink:
 

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