\begin{definition}[Definition:Field Norm/Definition 1]
Let $K$ be a field and $L / K$ a finite field extension of $K$.
Let $\alpha\in L$.
By Vector Space on Field Extension is Vector Space, $L$ is naturally a finite dimensional vector space over $K$.
Let $\theta_\alpha$ be the linear operator:
:$\theta_\alpha: L \to L: \beta \mapsto \alpha \beta$
The '''field norm''' $\map {N_{L/K} }\alpha$ of $\alpha$ is the determinant of $\theta_\alpha$.
\end{definition}