Hi, could you, please, help me with the following problem.
I have a set of 2x2 and 3x3 Hermitian matrices (i.e. matrix == complex_conjugate(transpose(matrix))). So, they are all positively defined and all their eigenvalues are real positive numbers.
These matrices are always calculated from some 2- and 3-dimensional irreducible matrix representations returned by the Repsn IrreducibleAffordingRepresentation function (so Cyclotomics are always involved?).
It seems that, for a significant amount of cases, I am not able to calculate Eigenvalues / Eigenvectors / Eigenspaces in GAP (e.g. I get truncated or completely empty lists of eigenvalues). I suspect then that, in general, this is simply not possible in GAP (and I will need to ask Mathematica to do it afterwards). Could you, please, confirm / deny this statement?
Two examples of such matrices are given below (well, the second one is a 4x4 matrix but I chose it for its "simplicity"; in general I really need 2x2 and 3x3 cases only):
[ [ 3, -E(15)-E(15)^2-E(15)^4-2*E(15)^7-E(15)^8-2*E(15)^11-2*E(15)^13-2*E(15)^14 ], [ -2*E(15)-2*E(15)^2-2*E(15)^4-E(15)^7-2*E(15)^8-E(15)^11-E(15)^13-E(15)^14, 3 ] ]
[ [ 9/2, -3*E(3)-3/2*E(3)^2, 3*E(3)+3/2*E(3)^2, 0 ], [ -3/2*E(3)-3*E(3)^2, 9/2, 0, 3/2*E(3)-3/2*E(3)^2 ], [ 3/2*E(3)+3*E(3)^2, 0, 9/2, 0 ], [ 0, -3/2*E(3)+3/2*E(3)^2, 0, 9/2 ] ]
Thanks in advance, Best regards, Jacek. _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
