#4834: Return eigenvectors as members of a "normal" space instead of as members
of
an eigenspace
------------------------------+---------------------------------------------
Reporter: jason | Owner: jason
Type: defect | Status: needs_info
Priority: major | Milestone: sage-4.6.2
Component: linear algebra | Keywords:
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
------------------------------+---------------------------------------------
Comment(by rbeezer):
A workaround is to begin with symbolic matrices, which are now amenable to
eigenvector computations (albeit slowly). See #6934, #10346 (coming soon
to an official release). Then results (eigenvectors) are symbolic for
starters, so they play nicely with a symbolic expression like the variable
t.
{{{
sage: B=matrix(SR, [[1,2],[2,1]])
sage: spec=B.eigenvectors_left()
sage: spec
[(3, [(1, 1)], 1), (-1, [(1, -1)], 1)]
sage: v = spec[0][1][0]
sage: z = spec[1][1][0]
sage: z.parent()
Vector space of dimension 2 over Symbolic Ring
sage: var('t')
t
sage: v + t*z
(t + 1, -t + 1)
}}}
But I think an addition to the coercion system is still the best long-term
solution, since these symbolic eigenvalue computations are not real
robust.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4834#comment:6>
Sage <http://www.sagemath.org>
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