Characterization of singular values

Question

Let $A \in \mathbb R^{m\times n}$ and its singular values be denoted by $\sigma_1 \geq \sigma_2 \geq \ldots \sigma_n \geq 0$. Then $$ \sigma_i(A) = \min\{\|B \|_2\colon B \in \mathbb R^{m \times n}, \mathrm{rank}(A-B) \leq i-1 \}. $$ How is this characterization of singular values obtained, is there a reference about it?