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?
That would skirt around this issue, though I still think this issue
ought to be resolved.
Jason
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