Thread: Matrix problem

I'm interested in the eigenvalues of the matrix H. The general definition of H is:



Where

and
for 1<k<K. (ie its constant over k)

is the period, with .


In particular, when there are no intermediary between 0 and T, I need to get an answer for H of:



In trying to work this out, I figured that the general definition of H reduces to


If I use the transpose of R(T) instead, I can manage to get



Which is close but not quite right. I think I'm going wrong in reducing the general definition down to my specific case, but don't know exactly what to do. Any ideas? Please tell me if i haven't been clear.

Also, what would happen to the eigenvalues if i just switched the signs of the coefficients in the last matrix to get what i wanted?

(Btw, thats meant to be a matrix multiplication up there, but the matrices misaligned for some reason.)

Many thanks