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Aug 26, 2015 at 6:10 comment added user1688 And also, you cannot expect the numeration of the eigenvallues being ascending for both operators. Say you have them ascending for one, then the other will preserve the eigenspaces and have its own eigenvalues there, so you can simultaneously diagonalize, but not both is ascending order.
Aug 25, 2015 at 22:05 comment added Matthias Ludewig that is obvious, yes
Aug 25, 2015 at 16:14 comment added user1688 Yes, if the operators commute.
Aug 25, 2015 at 10:07 history asked Matthias Ludewig CC BY-SA 3.0