Let S Mnxn(R) and D Mnxn(R) be n n matrices such that DTSD = S
where S is non degenerate. Let be an eigenvalue of with eigenvector
(i) Show that Sx is an eigenvector of DT and find its eigenvalue.
(ii) Show that is an eigenvalue of D.
[Hint: det(A) = det(AT ) for any square matrix A.]
This question has been giving me some real trouble and all help is welcome