Hi folks back again:
Bob, yes I said guess (which is the only strategy if one does not know
exactly). Here is what I found in:
Merriam-Webster's WWWebster Dictionary -includes definition (English),
illustration, phonic pronunciation, origin, thesaurus (indexed Oct 10 1997)
Main Entry: ei·gen·val·ue
Pronunciation: 'I-g&n-"val-(")yü, -y&(-w)
Function: noun
Etymology: part translation of German Eigenwert, from eigen own, peculiar +
Wert value
Date: 1927
: a scalar associated with a given linear transformation of a vector space
and having the property that there is some nonzero vector which when
multiplied by the scalar is equal to the vector obtained by letting the
transformation operate on the vector; especially : a root of the
characteristic equation of a matrix
Here are two links to Gauss:
http://www.treasure-troves.com/bios/Gauss.html
http://britannica.com/bcom/eb/article/1/0,5716,117281+2+109423,00.html
Herman here is what Britannica says:
"About 1820 Gauss turned his attention to geodesy--the mathematical
determination of the shape and size of the Earth's surface--to which he
devoted much time in theoretical studies and field work. To increase the
accuracy of surveying he invented the heliotrope, an instrument by which
sunlight could be utilized to secure more accurate measurements. By
introducing what is now known as the Gaussian error curve, he showed how
probability could be represented by a bell-shaped curve, commonly called the
normal curve of variation, which is basic to descriptions of statistically
distributed data."
Here is the history of matrices and determinants:
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/HistTopics/Matrices_a
nd_determinants.html
This source says that Gauss coined the term determinant, but not in the
meaning we use it today.
The origin and first use of "Eigenwert" eigenvalue unfortunately is not
discussed.
I guess(again in the same meaning as above) that Herman's explanation about
its origins is too complicated to be true,given
the whole history of matrices, but I may be wrong.
Bob you're right pointing to the problem that Gauss often claimed having
found something earlier, but not having it published.
He also was accused of plagiarism, but his diaries showed the contrary,
unless he had not falsified these (p<??).
Cohen: Jacob (Jack) Cohen is one of our heroes in psychology (and behavioral
sciences understood broadly):
Here is an obituary:
"Jacob Cohen made at least three major contributions to quantitative
methods, any one of which would have been enough to secure a world-wide
reputation as a leader in this field. Cohen�s kappa is cited in his
Distinguished Lifetime Contribution Award as "the gold standard for the
measurement of agreement between categorical judgments." He championed the
use of multiple regression as a general data�analytic framework,
illustrating the relationships between what are often treated as separate
methods of analysis, and he developed multivariate analogs (e.g., set
correlation) that allowed researchers to apply the regression framework to
virtually any data-analytic problem in the social and behavior sciences.
Finally, his work in statistical power analysis changed the way we think
about the meaning of significance tests, and his emphasis on effect-size
measures foreshadowed the development of meta-analysis."
Here is a full obituary for Jack:
http://web.missouri.edu/~psycmm/bgnews/1998/msg00036.html
The cite for Jack's seminal paper is:
Cohen,J.(1968) Multiple regression/correlation as a general data analytic
system.Psychological Bulletin.(sorry don't have the
exact ref.not handy because I'm at home)
This developed into the bestseller with his wife Patricia:
Cohen, J., & Cohen, P. (1983). Applied multiple regression/correlation
analysis for the behavioral sciences (2nd edition). Hillsdale, NJ: Erlbaum.
Jack once told me that the 1968 paper was almost not published due to the
resistance of the editors who where all educated
in seeing a real split between ANOVA and regression as maybe Elliot still
sees it.
BTW: Switzerland had had Euler on their 10Franken bill(6th banknote series
1976):
http://www.snb.ch/e/banknoten/alle_serien/alle_serien.html
Euler's bio is here:
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Euler.html
There is no reason for any national pride.All the giants are standing on the
shoulders of other normal people and other giants and that pyramid is truly
international!
But it would be nevertheless interesting just in case the new "too close to
call" President of the United States proposes
to put a leading figure from science and one from math/statistics on dollar
bills, just to have a cheap intervention to boost
the attitude towards science and math/statistics, whom would you propose?
If I had a vote my choices would be:
Richard Feynman and John Tukey.
Werner
Werner W. Wittmann;University of Mannheim; Germany;
e-mail: [EMAIL PROTECTED]
-----Ursprüngliche Nachricht-----
Von: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED]]Im Auftrag von Bob Wheeler
Gesendet: Sonntag, 21. Januar 2001 02:21
An: [EMAIL PROTECTED]
Betreff: Re: AW: eigenvalue: origin of term
Your national pride does you credit. Gauss was one
of the greats, and he may have used "eigenvalue"
or its equivalent, but I don't know for sure -- do
you really, or are you guessing?
It is hard to be certain with Gauss, because of
his brilliance, but I doubt that he used the
general linear model as we now know it, and
although he did solve least squares equations, he
may not have have invented the technique --
Legendre was the first to publish in 1809. No one
has been able to verify Gauss' use of least
squares before Legendre, because he either made
calculational errors in his analysis or used
something other than least squares. Gauss often
said in his later years upon being shown a new
technique, that he had used it himself but had not
published. Who is to say.
However, your 10DM bill to the contrary, Gauss was
not the first to use the normal distribution:
DeMoivre used it as an approximation the the
binomial about 50 years before Gauss was born.
The thrust of Fisher's ANOVA was in the
partitioning of sums of squares and in the use of
significant tests there upon -- brilliant ideas.
The fact that some of the computations can be done
with linear models does not make the procedures
equivalent, and Fisher's early papers clearly show
that he was well aware of the connection.
Calculation was no great problem. Pearson once
said, while twiddling the handle of his
calculator, that he had never encountered a
calculation too difficult for him; and his tables
of various functions are still as extensive and as
accurate as any produced by modern computers.
I can't find a paper by anyone named Cohen with a
title resembling what you give in CIS. Perhaps you
can improve the citation.
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