  An error analysis result is given for classical Gram--Schmidt factorization
of a full rank matrix $A$ into $A=QR$ where $Q$ is left orthogonal (has
orthonormal columns) and $R$ is upper triangular. The work presented here shows
that the computed $R$ satisfies $\normal{R}=\normal{A}+E$ where $E$ is an
appropriately small backward error, but only if the diagonals of $R$ are
computed in a manner similar to Cholesky factorization of the normal equations
matrix.
  A similar result is stated in [Giraud at al, Numer. Math.
101(1):87--100,2005]. However, for that result to hold, the diagonals of $R$
must be computed in the manner recommended in this work.
