#8974: Added eigenvalues, eigenvector, eigenspaces and minpoly to vector space
endomorphisms
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Reporter: mmarco | Owner: jason, was
Type: enhancement | Status: needs_work
Priority: trivial | Milestone: sage-4.4.4
Component: linear algebra | Keywords: eigenvalues
Author: Miguel Marco | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Changes (by davidloeffler):
* status: needs_review => needs_work
Comment:
Hmm. This is certainly functionality that we should have, but I don't
agree with the implementation: I strongly feel that these linear-algebra
methods should have *identical* behaviour for a matrix and for the
corresponding morphism object. Your {{{eigenvectors}}} method takes an
argument and returns the eigenvectors for that given eigenvalue, which
isn't what the matrix one does. Similarly, {{{eigenspaces}}} for matrices
makes a field extension if the eigenspaces aren't defined over the base
field, while yours just returns the empty list.
Also, the underlying implementation should just call the existing one
rather than doing the linear algebra anew. (E.g. for computing
eigenvectors I think there are nasty cases with badly-conditioned matrices
where just computing the kernel of X - lambda * identity blows up, and one
can work around this using various devious tricks; it's not great if we
have two different eigenvector methods and we have to fix them both
separately.)
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8974#comment:2>
Sage <http://www.sagemath.org>
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