#6942: jordan_form with transformation=true returns non-invertible
transformation
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Reporter: syazdani | Owner: tbd
Type: defect | Status: needs_info
Priority: critical | Milestone: sage-4.3.2
Component: linear algebra | Keywords: jordan_form, transformation
Author: Sebastian Pancratz | Upstream: N/A
Reviewer: Rob Beezer | Merged:
Work_issues: |
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Changes (by newvalueoldvalue):
* status: needs_review => needs_info
* reviewer: => Rob Beezer
* author: => Sebastian Pancratz
Comment:
Hi Sebastian,
Very nice!
1. One line in a list indented one-too-many characters. Fix in reviewer
patch for your convenience. Accept or not.
2. Most of the linear algebra matrix decompositions return all the
pieces, all the time. I've always thought it inconsistent Jordan form has
this {{{transformation}}} switch, sometimes returning one matrix, other
times two. Now would be a good time to change this behavior. But I see
that the form is almost a combinatorial routine (once you have the
spectrum), while the basis vectors require a whole lot more work, so maybe
best not to compute it unless it is asked for?
3. The list {{{Vsmall+Y}}} ends up in a {{{span()}}} in the
"vector_in_difference" routine. The span has an {{{already_echelonized}}}
switch, so I spent a lot of time trying to decide how (or if it was
possible) to somehow "keep" {{{Vsmall+Y}}} echelonized, since {{{Vsmall}}}
will start that way. Couldn't see a reasonable way to do anything too
clever, though.
4. Do you want the 10x10 matrix above for the doctests? I'd be happy to
package it up with the one-character patch. ;-)
Other than the doctest fix, this is ready to go. If you want to accept
the doctest fix, then go ahead and mark this as "positive review" -
everything else is just for your consideration.
Great to see all your good work since the summer, including this.
Rob
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6942#comment:8>
Sage <http://www.sagemath.org>
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