Find the singular value decomposition of $uv^T$

Question

Let $u$ and $v$ be vectors in $\Re^n $. Let $A= uv^T$ be the outer product of those vectors. How can i find the singular value decomposition of A in terms of $u$ and $v$?

Answer 1

If either $u$ or $v$ is equal to $0$. The situation is easy.

Otherwise $$A = \left(\frac{u}{\|u\|} \right)(\|u\|\|v\|) \left(\frac{v}{\|v\|}\right)^T$$