#12514: default behavior of matrix([...]).eigenvectors_right() should be sane
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Reporter: ppurka | Owner: jason, was
Type: defect | Status: new
Priority: major | Milestone: sage-5.0
Component: linear algebra | Keywords: matrix eigenvectors
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Comment(by rbeezer):
(2): This just a typo in the method name used in the example.
{{{
matrix( [ [1.0, 0], [0.1, 2.0] ] ).right_eigenvectors()
}}}
will behave identically to (1). (Note plural.)
(4): I have never liked the use of Sequence with `cr=True` for the basis
vectors of an eigenspace in these calls. IIRC, it would be easy to strip
out, but a bunch of doctests would need reformatting. In fact, right now
it is *harder* to doctest this sort of output for large instances since
the output from Sequence does not include as many whitespace characters
that can be used to rearrange the output. This might be a good question
to pose to sage-devel with an eye to removing it?
(1) vs (3): For RDF/CDF matrices there is no notion of a geometric
multiplicity for an eigenvalue. You will see that every eigenvalue comes
back with a single eigenvector, implying that they have geometric
multiplicty one. So changing the base ring to RDF/CDF should be a
conscious decision, in my mind. The current "problem" with (1) is that
absent a specified base ring, the choice is made to use RR, not RDF, and
matrices over RR are not as capable as over RDF:
{{{
sage: A = matrix([ [2, 1], [1, 2.0]])
sage: A.base_ring() == RR
True
}}}
Maybe the error message in (1) could be improved to specifically suggest
RDF, CDF or SR?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12514#comment:1>
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