3 Low rank approximation of the covariance matrix [2.5 pt] For a matrix M, if it admits eigenvalues, we denote them A1(M) 2 12(M) 2 .. . 2 Ad (M). Consider i.i.d. data D = {X1, ..., X,] with X, E Rd and define their mean X,, and their covariance matrix En = = [ ( X, - X..) ( X. _ x. ) and an eigenvalue decomposition En = Vdiag(Mi (E,), A. ().). . . . . AM The objective is to show that 5,6) = V diag(Al (En). A2 (D.). . . . . AL.).0. 0. . .. .0)1