Consider a Cholesky factorization of the matrix appearing in the normal equations for A E R^mxn, A^T ALL^T. Show that the columns of the matrix AL ^-T are orthonormal. In other words, this matrix is orthogonal in the case m = n. Next, based on this fact, describe how to construct a reduced QR factorization of A using the Cholesky factorization of A^TA.

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