Category:Realifications of Complex Vector Spaces

This category contains results about Realifications of Complex Vector Spaces.
Definitions specific to this category can be found in Definitions/Realifications of Complex Vector Spaces.

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 $X$.