Diophantine Geometry: An Introduction
《Diophantine Geometry: An Introduction》 · 第 176 页 · Part B，Section B.2「Heights on Projective Space」，Definition
The absolute (multiplicative) height on $\mathbb P^n$ is the function $H:\mathbb P^n(\overline{\mathbb Q})\to[1,\infty)$, $H(P)=H_k(P)^{1/[k:\mathbb Q]}$, where $k$ is any field with $P\in\mathbb P^n(k)$. […] Note that (B.2.1(c)) ensures that $H(P)$ is well-defined independent of the choice of the field $k$.