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Let $V, W$ be nonzero finite dimensional vector spaces over $\mathbb{C}$. Let $m$ be the dimension of the space of $\mathbb{C}$-linear transformations $V \rightarrow W$, viewed as a real vector space. Let $n$ be the dimension of the space of $\mathbb{R}$-linear transformations $V \rightarrow W$, viewed as a real vector space. Then

  1. $n=m$
  2. $2 n=m$
  3. $n=2 m$
  4. $4 n=m$

     

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