On Fri, Dec 19, 2008 at 12:22 PM, Jason Grout
<jason-s...@creativetrax.com> wrote:
>
> Robert Bradshaw wrote:
>
>>> The problem comes up when the parent of v has a user-defined basis,
>>> instead of the standard basis:
>>>
>>> sage: v.parent()
>>>
>>> Vector space of degree 2 and dimension 1 over Rational Field
>>> User basis matrix:
>>> [1 1]
>>
>> Yes, you hit the nail on the head. Note that (for better or for
>> worse) multiplication by the identity matrix makes it forget the user-
>> defined basis.
>>
>> sage: A=matrix([[1,2],[2,1]])
>> sage: eig=A.eigenvectors_right()
>> sage: v=eig[0][1][0]
>> sage: t = var('t')
>> sage: I = A.parent()(1); I
>> [1 0]
>> [0 1]
>>
>> sage: parent(v*t)
>> Vector space of degree 2 and dimension 1 over Symbolic Ring
>> User basis matrix:
>> [1 1]
>> sage: parent(I*v*t)
>> Vector space of dimension 2 over Symbolic Ring
>> sage: A*v - I*v*t
>> (3 - t, 3 - t)
>
>
> It looks like eigenvectors are returned as the basis vectors of the
> eigenspace. Should they be returned as just plain old vectors instead?
Yes, definitely. Then we don't have create a whole bunch of different
vector spaces for no reason too.
-- William
> That would skirt around this issue, though I still think this issue
> ought to be resolved.
>
> Jason
>
>
> >
>
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org
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