Show that q2 and u span the same subspace where q2 is the, Econometrics

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Show that q2 and u span the same subspace where q2 is the

Consider the QR decomposition of the uncentered N × (p + 1) matrix X (whose first column is all ones), and the SVD of the N × p centered matrix X˜ . Show that Q2 and U span the same subspace, where Q2 is the sub-matrix of Q with the first column removed. Under what circumstances will they be the same, up to sign flips?

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