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seen Jun 4 '12 at 22:26

Jun
4
comment How do I keep the right ordering of eigenvalues using Eigensystem?
@DanieLichtblau I think this will do the job. Thanks a lot.
Jun
4
comment How do I keep the right ordering of eigenvalues using Eigensystem?
@rcollyer you are correct, but then I would need to check which U (see above) constructed form various arrangements of these eigenvectors gives me the exact same A back when performing the reverse matrix multiplication (again, see my previous comment).
Jun
4
comment How do I keep the right ordering of eigenvalues using Eigensystem?
@ Szabolcs For already diagonal matrices, Diagonal would work just fine indeed. For non diagonal matrices, there happens to be a correct ordering that matches that of the already diagonal ones (this has to do with the ordered basis set). I understand that mathematica has no way to tell what this ordering is and thus use an ordering by magnitude. Then let me put it this way: I want the eigenvalues/eigenvectors to be given in such an order so that when I build U, the diagonalizing matrix, I get: U^dagger x A x U = D, D being diagonal, and more importantly, U*D*U^dagger gives me A back.
Jun
4
comment How do I keep the right ordering of eigenvalues using Eigensystem?
Let me clarify. All my 3*3 matrices are given WRT an identical, ordered basis set. In my case the ordering matters because it relates to a certain physical system with three energy curves. For example, if B={{2,0,0},{0,-3,0},{0,0,2}} which is already diagonal, then the first eigenvalue 2 will correspond to (x1,y1), the second to (x1,y2) and the third to (x1,y3), where y1, y2 and y3 are three points on three different energy curves (in this case two of my eigenvalues are degenerate). If Eigensystem reorders my eigenvalues it becomes very complicated for me to tell these values apart.