Orthogonality

Definition

Two vectors of $n$ dimensions are orthogonal if their dot product is equal to zero.

$$\vec{f}\cdot \vec{g}=\sum _{k=1}^n{f}_k{g}_k=0$$

The orthogonality of two vectors is discrete. For two functions to be orthogonal on some interval $[a,b]$, they must be continuously orthogonal at all points on $[a,b]$:

$$⟨f,g⟩={\int }_a^{b}f(x)g(x)dx=0$$

This is the continuous equivalent to the dot product, and is the inner product.