Semilinearity

linear-algebra

Definition

Semilinearity

Let $V$ and $W$ be vector spaces over a field $F$.

A map $T:V\to W$ is semilinear if there exists a field automorphism $\sigma :F\to F$ such that

$$T(x+y)=T(x)+T(y),T(\alpha x)=\sigma (\alpha )T(x)$$

for all $x,y\in V$, $\alpha \in F$.