Timeline for Is there a method to simultaneously block-diagonalize a set of group matrices?
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12 events
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| Mar 15, 2015 at 22:45 | comment | added | user6818 | @DavidSpeyer And for the same set of matrices there seems to exist multiple different block diagonalizations. | |
| Mar 15, 2015 at 21:17 | history | edited | user6818 | CC BY-SA 3.0 |
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| Mar 15, 2015 at 21:09 | comment | added | user6818 | @DavidSpeyer I checked with an example that the similarity transformation that diagonalzies the center does not give the most irreducible decomposition of the other elements of the group. How does one find that basis which will do that? | |
| Mar 15, 2015 at 6:41 | comment | added | Student | May be one has to go to the center and do this repearedly on each block to get the full reduction. | |
| Mar 15, 2015 at 5:06 | comment | added | Student | In a given example if I find a similarity transformation which diagonalizes the center then that applied on everyone else doesn't produce the same block-diagonal structure. In an irreducible representation decomposition all the matrices should have the same block structure. | |
| Mar 14, 2015 at 20:23 | comment | added | user6818 | @DavidSpeyer I am working over complex numbers. So you say that I can just detect the centre of the group and diagonalize any one of them and this basis should simultaneously block-diagonalize the rest of the matrices? But finding the center is still a brute-force calculation - right? | |
| Mar 14, 2015 at 0:07 | comment | added | Steve Huntsman | Some old but rather explicit physics notes of mine on doing this in the context of a simple lattice gauge theory are here: drive.google.com/file/d/0ByTBBePgIzD0a3ZGSWt3aFlJS00/… | |
| Mar 13, 2015 at 23:49 | comment | added | David E Speyer | Wait, is this a group in characteristic zero? Then I would compute the center of this group algebra (linear algebra) and diagonalize the central elements (since they commute). | |
| Mar 13, 2015 at 21:44 | comment | added | user6818 | @DavidSpeyer Thanks! Isn't my case simpler than what that other question asks for? I am saying - lets say you have $8$ $4\times 4$ matrices given to you explicitly. Then what would you do? | |
| Mar 13, 2015 at 21:32 | comment | added | David E Speyer | See math.stackexchange.com/a/185001/448 . If someone reading this knows a better place to point people than my answers, please do so! | |
| Mar 13, 2015 at 21:30 | history | edited | user6818 | CC BY-SA 3.0 |
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| Mar 13, 2015 at 21:22 | history | asked | user6818 | CC BY-SA 3.0 |