Timeline for Find unitary transformation between two sets of matrices that represent group generators
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 3, 2021 at 23:24 | comment | added | Gerson J Ferreira | You mean that I need $A_i$ and $B_i$ to be irreps? If they are not irreps, then I guess that there will be multiple $U$s, but they will differ only by a phase between the subspaces defined by the irreps. In practice I plan to apply this to the case where $A_i$ and $B_i$ are direct sums of irreps. So it should be ok. | |
| May 3, 2021 at 23:24 | comment | added | Gerson J Ferreira | Indeed the unitary condition comes after. But in practice it is sufficient to find an $U$ that can be made unitary with a simple normalization, since I'm interested in the transformation itself, the determinant will always cancel in practice. I've implemented the code as described above and it seems to work well for the cases I've tested. It gives a single zero singular value. | |
| May 3, 2021 at 17:00 | comment | added | LSpice | If you want to speak of the eigenvector $\vec U$ (really the eigenline), then you'll want to require that the representation is irreducible. Otherwise there will be more than a line's worth of intertwiners, and the unitarity condition will be an extra quadratic (actually sesquilinear, because of the conjugation) constraint. | |
| May 2, 2021 at 22:35 | comment | added | daydreamer | I think this can be seen in the light of the orbit-stabilizer theorem, where U is the unknown whose right orbit (acted by A) equals the left orbit (acted by B). | |
| May 2, 2021 at 21:03 | history | answered | Gerson J Ferreira | CC BY-SA 4.0 |