Powers of a matrix of special type

In this paper it is shown that if ETE = I, i.e., if the columns of E are orthonormal, and K is a diagonal matrix with all terms positive, then (1) [/ 4-E(K -I)ETY -1 + E(Kn -I)ET for any real n.Since given any matrix V and a positive definite matrix G it is possible to find an E and K as just described satisfying