Q&A

• HW6 Q11.6 (MP inverse produces the smallest least squares solution). $\beta^\star = (\beta^\star - \beta^+) + \beta^+$, where $\beta^\star - \beta^+ \in \mathcal{N}(X’X) = \mathcal{N}(X)$ and $\beta^+ \in \mathcal{C}(X’)$. Thus $\beta^\star - \beta^+ \perp \beta^+$ and $|\beta^\star|^2 = |\beta^\star - \beta^+|^2 + |\beta^+|^2 \ge |\beta^+|^2$.

• HW4, Q3.5 (Householder transformation for QR decomposition).

• HW4 BV 12.2. (QR decomposition for least squares).

• HW5 BV 11.5(a).

• HW5 Q6.2.

• HW6 Q11.3, 11.5.