Let S M_{nxn}(R) and D M_{nxn}(R) be n n matrices such that D^{T}SD = S

where S is non degenerate. Let be an eigenvalue of with eigenvector

x.

(i) Show that Sxis an eigenvector of D^{T}and find its eigenvalue.

(ii) Show that is an eigenvalue of D.

[Hint: det(A) = det(A^{T}) for any square matrix A.]

This question has been giving me some real trouble and all help is welcome