Eigenvalues and Eigenvectors of the Rouse-Mooney Matrix

Appendix 9.C — Eigenvalues and Eigenvectors of the Rouse Mooney Matrix 

We consider the Rouse-Mooney matrix Mgt) of the dimension z x z. The z eigenvalues os of the matrix are the roots of the equation obtained by setting the determinant = Mgt — cw stl equal to zero, i.e. 

From Eq. (19.C.1), the recursion relation is found as follows with 

Following a procedure similar to that used in the Rouse matrix case, the normalized eigenvectors C (A = 0,1,2. — 1) corresponding to 

Appendix 9.D — Hierarchy and Universality among the Inherent Characteristic Times in the (Extended) 

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