Opened 10 years ago
Last modified 3 years ago
#11285 new enhancement
Request to add feature: Decomposing a finite dimensional vector space with respect to a collection of matrices acting on the vector space.
Reported by: | chrisjamesberg | Owned by: | AlexGhitza |
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Priority: | major | Milestone: | sage-wishlist |
Component: | algebra | Keywords: | days30, days88 |
Cc: | Merged in: | ||
Authors: | Reviewers: | ||
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
I would like to request a new feature for Sage. I would like to be able to input a collection of n by n matrices which I think of as acting on an n dimensional vector space and have sage output a decomposition of the vector space into irreducible components with respect to the action of these matrices.
addendum: it would even be better to have a method that provides the finest decomposition up to subgroups of finite index!
Attachments (1)
Change History (7)
comment:1 Changed 10 years ago by
- Summary changed from Request to add feature: Decomposing a finite dimensional vector space with respect to a collection of actions. to Request to add feature: Decomposing a finite dimensional vector space with respect to a collection of matrices acting on the vector space.
comment:2 Changed 10 years ago by
- Keywords days30 added
comment:3 Changed 8 years ago by
Changed 8 years ago by
comment:4 Changed 8 years ago by
Hi Travis,
You want to get in touch with Aladin, for this is decomposing a module for a general finite dimensional algebra, and he is working on the representation theory of those algebras.
comment:5 Changed 3 years ago by
- Keywords days88 added
comment:6 Changed 3 years ago by
- Description modified (diff)
I've uploaded the start of a patch which works well if the basis is suitably chosen. I just apply all the matrices and see where it takes the natural basis vectors, and merges into appropriate subspaces. In the documentation there is the start of a good test example if anyone can get this to work...