Suppose $A \in \mathbb{C}^{n \times n}$ and denote the singular values of $A$ by $\sigma\_1 \geq \cdots \geq \sigma\_n$. Prove that 
$$\sigma\_k = \underset{dim W = n-k+1}{\min} \underset{u \in W, ||u|| = 1}{\max}||Au||$$

I don't know how to start this proof. Any idea would be appreciated. Thanks in advance.