Hello,
In the following thread [1], was mentioned a problem with computation
of eigenvectors for matrices over number field. I get a similar bug
with sage-5.0 where sage answers a *wrong* eigenvector.
Let's take a simple example
{{{
sage: K.<c> = NumberField(x^2-x-1,'c',embedding=RR(1+sqrt(5))/2)
sage: m = matrix(K,[[0,-1],[1,c]])
sage: v = m.eigenvectors_right()
sage: l0 = v[0][0]
sage: v0 = v[0][1][0]
}}}
First of all, its not possible to multiply the vector by the matrix
{{{
sage: m * v0
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
...
TypeError: unsupported operand parent(s) for '*': 'Full MatrixSpace of
2 by 2 dense matrices over Number Field in c with defining polynomial
}}}
Then, much more dramatic, v0 is *not* at all the eigenvector of m
{{{
sage: m * vector(CC,v0) / l0
(1.00000000000000, -1.92705098312484 + 0.951056516295154*I)
sage: vector(CC,v0)
(1.00000000000000, 0.309016994374947 + 0.951056516295154*I)
}}}
I didn't find a ticket for that purpose (even if the old #82 seems
related to). Should I open a ticket ? How may I solve the issue ?
Best,
Vincent
[1]
http://groups.google.com/group/sage-devel/browse_thread/thread/f673dfac9047d4e9/c48047c705b13b3a
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