I want to know the steps of converting eq. 28 to eq. 30

you can find the the full document in

https://www.robots.ox.ac.uk/~cvrg/hilary2006/ppca.pdf

In the M-step, (Lc) is maximised with respect to W and of giving new parameter estimates W = [ (tn - nexx)" [(x x ) ]. (27) 2 1 = a [ filth - Hell? - 2(xn ) W' (tn - 10) + tr ((xax ) WW)} (28) To maximise the likelihood then, the sufficient statistics of the conditional distributions are cal- culated from (25) and (26), after which revised estimates for the parameters are obtained from (27) and (28). These four equations are iterated in sequence until the algorithm is judged to have U converged. We may gain considerable insight into the operation of the EM algorithm by substituting for (Xn) and (Xx,,) from (25) and (26) into (27) and (28). Some further manipulation leads to both the E-step and M-step being combined and re-written as: W = SW(o I + M-'W'sw)-1, (29) 62 = -tr (S- SWM-'W') , (30) where S is again given by S = ( tn - 1) (tn - Re). (31) 1 = 1