Definition:Field Norm

Definition
Let $K$ be a field and $L / K$ a finite field extension of $K$.

Then by Field Extension is Vector Space, $L$ is naturally a vector space over $K$.

Let $\alpha \in L$, and $\theta_\alpha$ be the linear map:


 * $\theta_\alpha: L \to L: \beta \mapsto \alpha \beta$

The field norm $N_{L/K} \left({\alpha}\right)$ of $\alpha$ is the determinant of this map.

Also see

 * Field Norm is Norm, proving that the field norm is in fact a norm.