Ok, thanks.
On 4 Sep., 20:53, "John Cremona" <[EMAIL PROTECTED]> wrote:
> Your construction gives a rank 1 matrix, so there's a double
> eigenvalue of zero. The two eigenvectors which are found for that
> eigenvalue need not be orthogonal, they are just some basis for the
> eigenspace. The entries you thought should be zero are the inner
> product of those eigenvectors with each other.
>
> It would be possible for the eigenvector/space functions to detect
> when a matrix was real and symmetric, and in that case return
> orthgonal eigenvectors, but that is not the way it is at present.
> Unless there are other functions which I don't know about.
>
> John Cremona
>
> 2008/9/4 chris75de <[EMAIL PROTECTED]>:
>
>
>
> > Hi,
>
> > the following code
>
> > b=matrix(3,1,[random() for i in [1..3]])
> > B=b*b.transpose()
> > lb,Sb=B.right_eigenvectors()
> > print lb
> > print
> > print Sb.transpose()*B*Sb
> > print
> > print Sb.transpose()*Sb
>
> > give's in my sage version 3.0.6 the following result:
>
> > [1.844328223, 4.46105473802e-17, -3.42287439238e-16]
>
> > [ 1.844328223 -1.11022302463e-16 2.91433543964e-16]
> > [-8.30521194918e-17 -3.99656191956e-18 2.92386038647e-19]
> > [ 2.73402117214e-16 2.893962297e-17 -5.58462128744e-17]
>
> > [ 1.0 -1.66533453694e-16 -7.6327832943e-17]
> > [-1.66533453694e-16 1.0 0.709678542323]
> > [ -7.6327832943e-17 0.709678542323 1.0]
>
> > I think the last matrix have to be the identity matrix, but there are
> > two times 0.709678542323 instead of zero.
>
> > Christian
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