TITLE: Is the matrix $R$ in the $QR$ decomposition unique?
QUESTION [5 upvotes]: 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 $R$.

REPLY [3 votes]: Yes, see this page. (it uses positivity in the middle, in case you wonder).