Circular Matrix Decomposition in MATLAB

Hello all,

I have this N-by-N circular matrix F. Theoretically, this matrix can be decomposed as F=WDW', where W is the direct DFT matrix and D is a diagonal matrix that contains the eigenvalues of F. In MATLAB I want to compute D as following:

D=(conj(dftmtx(N))/N)*F*dftmtx(N)

This should give me a diagonal matrix, which doesn't. Why?