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The Laplacian matrix is the representation of a graph in matrix form.

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Explicit eigenvalues of the Laplacian

Various authors comment that the spectrum of the Laplacian is not easy to determine explicitly, and much of the literature seems to be consumed only with estimates for certain eigenvalues of the Laplacian … Are there other interesting manifolds for which the spectrum of the Laplacian is known? In particular, are they known for ellipsoids? …