matrix is at first glance. However, it is easy to demonstrate that by a unitary transformation, this matrix is equivalent to:Which can be verified directly by numerically (or for purists, analytically - see Chebyshev polynomials for some clues) diagonalising the sub-matrix formed by removing the first row and column. Rotating the basis defining this sub matrix using the resulting unitary brings the original matrix into the originally stated form. This matrix has a P4 permutation symmetry, which in this basis is much easier to see, and could constitute a 'hidden' symmetry. In this case, there are no degeneracies in the eigenspectrum. The technical reason for this is that each eigenstate transforms with respect to a different irreducible representation of P4. If one encountered a case where some group of eigenstates correspond to the same irreducible representation of the 'hidden' symmetry group, a degeneracy would be observed. Although for this simple 4x4 matrix the symmetry could have been guessed (it was after all, always there to begin with), if the matrix was larger, it would have been more difficult to spot. See also Renormalization External links Accidental Symmetry in Quantum Physics Quantum field theory References