I'd like to know for positive diagonal elements why is $R$ in $QR$ decomposition unique.
My guess is it must have something to do with linearly independence of the column of $R$, but then I can think of a property that lead me to uniqueness of $R$.
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1$QR=Q'R'$ iff $Q'^{-1}QR=R'$ – Hagen von Eitzen Jan 11 '14 at 19:49
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2@HagenvonEitzen: Whoa, easy peasy! But what's the role of positive diagonal elements in your proof? – Gigili Jan 11 '14 at 19:55
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Yes, see this page. (it uses positivity in the middle, in case you wonder).
Igor Rivin
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Sorry, but the link is down. Can you share the response or another link? – lithiium Dec 02 '14 at 04:01
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1One part of proof on link I think is wrong? They write $\frac{\alpha_i}{\beta_i} = \frac{\alpha_i}{\beta_i}$. But, do they mean to say $\frac{\alpha_i}{\beta_i} = \frac{\beta_i}{\alpha_i}$? – Frank Jun 14 '20 at 21:48
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