A Course in Finite Group Representation Theory
《A Course in Finite Group Representation Theory》 · 第 189 页 · Section 4.7「Norm and Trace」，Definition 1
Let $L/K$ be a finite field extension. For elements $a\in L$, consider the multiplication map $\varphi_a:L\to L$, $x\mapsto ax$, as an endomorphism of $L$ as a $K$-vector space. Then $\operatorname{tr}_{L/K}(a):=\operatorname{trace}(\varphi_a)$, $N_{L/K}(a):=\det(\varphi_a)$ are called the trace and the norm of $a$ with respect to the extension $L/K$.