Definition:Realification of Complex Vector Space

Definition
Let $\struct {X, +, \circ}$ be a vector space over $\C$.

Define $\circ_\R : \R \times X$ such that:


 * $\lambda \circ_\R x = \lambda \circ x$

for each $\lambda \in \R$, $x \in X$.

We say that the $\R$-vector space $X_\R = \struct {X, +, \circ_\R}$ is the realification of $X$.