Talk:Realification of Normed Dual is Isometrically Isomorphic to the Normed Dual of Realification

The underlying set is the same with both $X$ and $X_\R$, all we are doing is restricting the scalars to $\R$. For example, for $x \in X$ we still have $ix \in X_\R$, but in the realification $X_\R$ the element $i x$ cannot be obtained just by multiplying $x$ by $i$. This is why $\C^n$ has dimension $n$ as a vector space over $\C$ but its realification has dimension $2 n$. Caliburn (talk) 23:39, 15 June 2023 (UTC)