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From: amy666 on 25 Dec 2008 08:05
> Gottfried wrote :
>
> > Am 25.12.2008 22:00 schrieb Gottfried Helms:
> > > then there is a non-invertible matrix W where
> > >
> > > P~ * W = W * E // E is
> > diag(1,e,e^2,e^3,...)
> > >
> > > and W is the vandermonde-matrix
> > > W = matrix(r=0..inf,c=0..inf c^r/r! )
> > //r=rowindex,c=ol-index
> > >
> > It should be noted as a curiosity, that P is
> > a triangular matrix with unit-diagonal. For finite
> > dimension the eigenvalues for such a matrix are
> > uniquely determined and they equal the entries of
> the
> > matrix-diagonal.
> > In the case of infinite dimension, using a somehow
> > "generalized" eigenvector-matrix, it seems, we can
> > have eigenvalues, which differ from the triangular
> > matrix-diagonal. So we have a nice example here
> for
> > a new property of infinite matrices compared to
> > finite matrices.
> >
> > This is even more interesting, since we had from
> the
> > diagonalization-approach to tetration, that we
> > expected
> > *different* (infinite) sets of eigenvalues, which
> > reflect
> > the different possible fixpoint-shifts. From the
> > consideration
> > of finite matrices we could not even think about
> > different sets
> > of eigenvalues...
> >
> > Hmmm...
> >
> > Gottfried Helms
>
> hmm
>
> is there a name for this property ?
>
> or is this what you call fixpoint shift ?
>
> i cant find much about infinite matrices ...
>
> the concept only seems to occur in connection to
> tetration ?
>
> intresting.
>
> perhaps post it to tetration forum.
>
> and give me some credit , since i came with A^C :)
>
>
> marry Xmas
>
> regards
>
> tommy1729

someone wrote a paper about the diverging of solution limits to tetration.

he was more into series but i think its an analogue.

cant remember his name though.

regards

tommy1729
From: amy666 on 25 Dec 2008 08:02
Gottfried wrote :

> Am 25.12.2008 22:00 schrieb Gottfried Helms:
> > then there is a non-invertible matrix W where
> >
> > P~ * W = W * E // E is
> diag(1,e,e^2,e^3,...)
> >
> > and W is the vandermonde-matrix
> > W = matrix(r=0..inf,c=0..inf c^r/r! )
> //r=rowindex,c=ol-index
> >
> It should be noted as a curiosity, that P is
> a triangular matrix with unit-diagonal. For finite
> dimension the eigenvalues for such a matrix are
> uniquely determined and they equal the entries of the
> matrix-diagonal.
> In the case of infinite dimension, using a somehow
> "generalized" eigenvector-matrix, it seems, we can
> have eigenvalues, which differ from the triangular
> matrix-diagonal. So we have a nice example here for
> a new property of infinite matrices compared to
> finite matrices.
>
> This is even more interesting, since we had from the
> diagonalization-approach to tetration, that we
> expected
> *different* (infinite) sets of eigenvalues, which
> reflect
> the different possible fixpoint-shifts. From the
> consideration
> of finite matrices we could not even think about
> different sets
> of eigenvalues...
>
> Hmmm...
>
> Gottfried Helms

hmm

is there a name for this property ?

or is this what you call fixpoint shift ?

i cant find much about infinite matrices ...

the concept only seems to occur in connection to tetration ?

intresting.

perhaps post it to tetration forum.

and give me some credit , since i came with A^C :)


marry Xmas

regards

tommy1729
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