= Reduced QR least-squares solution
{title2=$Rx=Q^Tb$}
Let $A=QR$ with $Q^TQ=I$ and square invertible upper triangular $R$. The <normal equations for linear least squares> reduce from $R^TRx=R^TQ^Tb$ to the system in the title. It is solved by <back substitution>. The geometric identity $\|Ax-b\|_2^2=\|Rx-Q^Tb\|_2^2+\|(I-QQ^T)b\|_2^2$ proves existence and uniqueness of the minimizer. For tall $Q$, $QQ^T$ is an <orthogonal projection>, not the identity on the entire observation space.
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