Perturbations on the Matrix

The following stationary perturbation theory on the matrix A is also derived from the direct analogy of the present case to that of quantum mechanics.  

Let eA be the perturbation on the unperturbed matrix A q, where e is some parameter. Expanding the perturbed eigenvectors and eigenvalues in power series in s, one obtains  

The orthogonality relation (6) simplifies (102) and finally one obtains the following equations for the non-degenerate system  

In the case in which there exists the backward transition at the (N A- l)th well. A is an (AT - - 1) x N 1) matrix with all zero 

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