Linear least-squares problem (${\min }_x\Vert Ax-b{\Vert }_2$)

A linear least-squares problem minimizes $\Vert Ax-b{\Vert }_2$ over $x$. If $A=QR$ has full column rank, orthogonality reduces it to the upper-triangular system formed from the leading block of $R$ and the leading entries of $Q^{T}b$.