Q1.
(a) Let \hatUj be the j-th component of \hatU. Show that \mathcalL = \mathcalLmax if and only if \hatUj = α for all j = 1, 2, \dots, n.
(b) Let α = 2. Show that \hat{\mathbfS}max = \mathbfSmax \mathbfSmax and the state \mathbbRn.
(c) Show that \mathcalL_{\mathcalA}(\mathcalA) = \mathcalL_{\mathcalA}(\mathcalA).
(d) Show that \mathcalO(\mathbbRn) \sim 10-11.
(e) Show that \mathcalO(\mathbbRn) \sim 10-10.