Hello, let A=I+a*K where "I" denotes kxk identity matrix, "K" denotes kxk matrix where all elements are 1 and "a" denotes a scalar. Let y be any kx1 vector and X be any kxn matrix. Let z=y'AX(X'AX)^(-1) X'Ay. Obviously z is a scalar. But what is its form related to "a". Is it polynomial of "a", or fraction of polynomials of "a"? What are the degrees of the polynomials? I will be very glad for any help. Thanks a lot.