Diophantine Geometry: An Introduction
《Diophantine Geometry: An Introduction》 · 第 174 页 · Section B.2「Heights on Projective Space」，Definition
Let $k$ be a number field and $P=(x_0,\ldots,x_n)\in\mathbb P^n(k)$. The height of $P$ relative to $k$ is $H_k(P)=\prod_{v\in M_k}\max\{\|x_0\|_v,\ldots,\|x_n\|_v\}$; the text calls $H_k$ the multiplicative height.