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NOTE: The original post to which this thread refers may be
seen at:
http://people.ne.mediaone.net/ghammond/MeasureGod.html
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gordon brown wrote:
>
> On Wed, 11 Jul 2001, George Hammond wrote:
>
> > No, in general the Rank (R) of an NxN matrix is not the
> > same as the Order of the matrix which is by definition, N.
> > The number of evigenvalues and eigenvectors is equal
> > to the Rank, not the Order. Naturally these R eigenvectors
> > are non-zero or we wouldn't be talking about them. If you
> > want to insist that there are actually N, but N-R of them
> > are "zero eigenvectors", ok, but like I said I'm not here
> > to jawbone about trivia.
>
> George,
>
> The rank of a matrix is the dimension of the space spanned by its columns
> (or, equivalently, by its rows).
GH: It is the dimensionality of the scalar product space
of the matrix, period. At least in the case of real
symmetric matrices.
> In the special case of a diagonal matrix
> this would be the number of non-zero columns (or rows), i. e. the number
> of NON-ZERO eigenVALUES counted with multiplicity.
GH: Any real symmetric matrix can be diagonalized, and in the
case of experimental matrices multiplicity is never
encountered and need not be considered.
> Thus, for a
> diagonalizable matrix (such as a real symmetric matrix) the rank is also
> the number of non-zero eigenvalues counted with multiplicity.
GH: Everyone knows that including the whole of Factor Analysis
and me... practical scientists take that for granted and is
certainly the only explanation for the fact that the Rank can
be less than the Order, which is the founding principle of
Factor Analysis.
> You seem to have eigenvectors and eigenvalues confused in your discussion.
GH: Don't be ridiculous, there is one eigenvector for each
eigenvalue, since all of the eigenvalues are distinct in
experimental psychometry. Please forego the tempting
stratagem of trying to turn this discussion of the
experimental discovery of God into a trivial pure
mathematics discussion. There is no issue there
and it's irrelevant.
> Gordon Brown
> Department of Mathematics
> University of Colorado
> Boulder, CO 80309-0395
[Hammond]
I don't have anything confused Gordon. The only point of confusion is
that no one on this list is able to discuss the point of my post
http://people.ne.mediaone.net/ghammond/MeasureGod.html
which is about the relevance of eigenvectors to God, instead, what they
want to do is start an argument about algebra and trigonometry which is
something more commensurate with their personal interests apparently
and hardly relevant to the issue.
I said (FAPP) that a 1000x1000 real symmetric matrix had
"13-eigenvectors",
which is a legitimate statement based on the fact that the Rank of a
1000x1000 matrix could certainly be 13. This is a correct statement.
Stein Somme quibbled that no, the number of eigenvectors would have to be
1000 not 13.... he is wrong, and you are confused. Your statement is
nothing but a restatement of my statement in different words. His argument
was wrong to begin with, and both of you are contributing nothing to
the point of the discussion.
Finally, the theory of matrices is so well known to Factor Analysis
that it has been written into commercial computer programs. It is
a documented fact, that of 100,000 published Factor Analyzed Psychometry
matrices in the past 40 years, 90% of them had a RANK approximately
equal to 1/2 of their ORDER, or less, (R <= .5N). So you are
quibbling with the existence of a fact that is as well known and
documented as the length of the Great Wall of China.
It is absolutely clear that I know what I am talking about, that the
facts and the mathematics are not in question, that a discussion about
elementary matrix mathematics is irrelevant, and that Factor Analysis
is such a well trodden and established field that trying to take issue
with it on the basis of elementary matrix theory amounts to no more
than an attempt at pedantic harassment. Lets stay on the subject,
which is the proposition that, experimentally, Hammond has asserted
that:
"God is provable as a psychometric eigenvector".
This discovery of course, is the only reason that we are wading through
all this mathematics.... all the way to Einstein's (linearized)
Tensor mathematics, never mind linear algebra. After all, the Poets
are not going to prove God, the scientists and mathematicians are,
and that includes psychologists as scientists BTW.
-- Be sure to visit my website below, and please ask your news service provider to add alt.sci.proof-of-god ----------------------------------------------------------- George Hammond, M.S. Physics Email: ghammond@mediaone.net Website: http://people.ne.mediaone.net/ghammond/index.html -----------------------------------------------------------
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