# Definition:Orthogonal (Linear Algebra)/Euclidean Space

## Definition

Let $\mathbf{u}$, $\mathbf{v}$ be vectors in $\R^n$.

Then $\mathbf{u}$ and $\mathbf{v}$ are said to be orthogonal iff their dot product is zero:

$\mathbf{u} \cdot \mathbf{v} = 0$

As Dot Product is Inner Product, this is a special case of the definition of orthogonal vectors.