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I am trying to show that for any $n\times m$ matrix $A$ and a vector $v$ in $\mathbb R^m$, that equivalence $Av = 0 \iff A^TAv = 0$.

I am really sure where to start with this one. Can youall offer some hints to get me started?

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1 Answer 1

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$(\Longrightarrow)$ is trivial.

$(\Longleftarrow)$ Assume $A^TAv = 0$, then also $v^TA^TAv = \|Av\|^2=0$ and hence $Av = 0$.

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