# Geometry

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# The Geometry of Euclidean Space

## Vectors in n-space

### Cauchy–Bunyakovskii–Schwarz Inequality

Let $x,y$ be vectors in $R^n$. Then

$|x<y| \leq ||x||||y||$

### Triangle Inequality

Let $x,y$ be vectors in $R^n$. Then

$||x+y|| \leq ||x||+||y||$

# Next steps

Linear Algebra

Vector Calculus