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 $v$?
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If either $u$ or $v$ is equal to $0$. The situation is easy.
Otherwise $$A = \left(\frac{u}{\|u\|} \right)(\|u\|\|v\|) \left(\frac{v}{\|v\|}\right)^T$$
Siong Thye Goh
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But what if i want to represent it as $n×n$ matrixes $U$ $\sum$ and $V$? – JustANoob Sep 07 '17 at 09:32
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Use gram-schmit process to extent the basis. – Siong Thye Goh Sep 07 '17 at 09:35