Deduce that the linear transformation (Y mapsto L Y=hat{mu}=X hat{beta}) is a projection (mathcal{H} ightarrow mathcal{H}), but

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Deduce that the linear transformation \(Y \mapsto L Y=\hat{\mu}=X \hat{\beta}\) is a projection \(\mathcal{H} ightarrow \mathcal{H}\), but not an orthogonal projection unless \(Q \mathcal{X}=\mathcal{X}\).

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