On Nov 20, 2007 11:14 AM, David Joyner <[EMAIL PROTECTED]> wrote:
>
> Hi:
>
> Something funny is going on:
>
> sage: MS = MatrixSpace(CC, 2, 2)
> sage: A = MS([[1,5],[3,-1]])
> sage: A.eigenspaces()
>
> [
> (4.00000000000000, [
> (1.00000000000000, 1.00000000000000)
> ]),
> (-4.00000000000000, [
>
> ])
> ]
> sage: A.eigenspaces()[0]
>
> (4.00000000000000, [
> (1.00000000000000, 1.00000000000000)
> ])
> sage: A.eigenspaces()[1]
>
> (-4.00000000000000, [
>
> ])
> sage: MS = MatrixSpace(QQ, 2, 2)
> sage: A = MS([[1,5],[3,-1]])
> sage: A.eigenspaces()
>
> [
> (4, [
> (1, 1)
> ]),
> (-4, [
> (1, -5/3)
> ])
> ]
>
> I find it strange that eigenspaces works for QQ
> but not for the larger field CC. Makes me think
> the problem isn't with eigenspaces at all ...
> Should I create a trac item under linear algebra
> or ???
Yes make a trac ticket. The issue above is undoubtedly that
there is no specialized implementation of matrices over CC.
It's just completely generic code. So some generic echelon
is going wrong. If you want something that actually works
very efficiently now, use CDF, which has the advantage that
it will scale to HUGE problems:
{{{id=0|
m = matrix(CDF,[[1,5],[3,-1]])
}}}
{{{id=1|
m.eigenspaces()
///
([4.0, -4.0], [Vector space of degree 2 and dimension 1 over Complex
Double Field
User basis matrix:
[ 0.707106781187 -0.514495755428], Vector space of degree 2 and
dimension 1 over Complex Double Field
User basis matrix:
[0.707106781187 0.857492925713]])
}}}
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