Inner Product

Inner Product of Functions

Analogous to the dot product of vectors $\sum \_{k=1}^{n}v\_ku\_k$. The inner product of two functions is a number and denoted by $⟨f,g⟩$.

$$⟨f,g⟩=\int \_0^{2\pi }f(x)g(x)dx$$

Just like with vectors, the inner product of functions with itself is equal to the square of the functions norm: $⟨f,f⟩=||f|{|}^2$