標準内積 standard inner product

$n \geq 0$ を自然数としたとき,\[x = (x_{1},\ldots,x_{n}),y = (y_{1},\ldots,y_{n}) \in \mathbb{R^{n}}\]に対して,\[\langle x,y \rangle = x_{1}y_{1} + \ldots + x_{n}y_{n} \in \mathbb{R}\]を,$x$ と $y$ の標準内積[standard inner product]といいます.

Mathematics is the language with which God has written the universe.