In the text I asserted that the first-order corrections to an ≪-fold degenerate energy are...

In the text I asserted that the first-order corrections to an ≪-fold degenerate energy are the eigenvalues of the W matrix, and I justified this claim as the "natural" generalization of the case n = 2. Prove it, by reproducing the steps in Section 6.2.1, starting with

(generalizing Equation 6.17), and ending by showing that the analog to Equation 6.22 can be interpreted as the eigenvalue equation for the matrix W.