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He showed that in this case the integral equation had real eigenvalues, and the solutions corresponding to these eigenvalues he called eigenfunctions.
Upon diagonalization of C, a set of eigenvalues and eigenvectors is generated defining a new set of generalized coordinates.
In a very natural way, concepts of linear algebra, including eigenvalues and eigenvectors, appear.
In particular he proved results on the existence of matrices with given eigenvalues and given diagonal elements.
This is where those eigenvalues of random Hermitian matrices enter the picture.
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