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Fortunately, LAPACK provides routines to deal with the $\mathbf Q$ factor from the $\mathbf A = \mathbf Q \mathbf R$ decomposition, [dgeqrf]. To find the projection of an arbitrary $\mathbf B$ onto the space orthogonal to $ \mathrm {range}(\mathbf A)$, you want to form $\mathbf C = \left(\mathbf I - \mathbf Q \mathbf Q^T\right) \mathbf B$. Here are two ...

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