In one of the homeworks that I am dealing with for Linear Systems course, I have encountered with such a statement: Consider $C^N$ the vector space of N dimensional complex vectors. We can define a basis
F={f1,...,fN} where
\begin{align}
f_k = \begin{bmatrix}
 f_{k,1} \\
 f_{k,2} \\
 .\\
 .\\
 f_{k,N} 
\end{bmatrix}
\end{align}

and $f_{k,l} = \frac{1}{N}e^{\frac{j2\pi(k-1)(l-1)}{N}}$. It is straightforward to show that those vectors are orthogonal, but I have no idea about how to show that those vectors are linearly independent, and their span is $C^N$. Could you please give me a clue?