In article <[EMAIL PROTECTED]>,
Werner Wittmann <[EMAIL PROTECTED]> wrote:
>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: eigenvalue
>Pronunciation: 'I-g&n-"val-(")y, -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
We certainly have much older uses of characteristic values
and characteristic vectors. The theorem that a matrix
satisfies its characteristic equation is usually called the
Cayley-Hamilton Theorem. This definitely dates it to the
19th century. It could be that the first use of eigenvalue
is 1927, but this does not change the date problem. Also,
why is the characteristic equation not called the eigen
equation, or something similar?
>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."
The normal distribution goes back to de Moivre, who obtained
it as the limit of binomial distributions; the paper is more
than 46 years before Gauss was born. The use of the normal
distribution to obtain least squares from maximum likelihood
considerations goes back to before 1800; I believe that Gauss
claimed he had it back then.
Gauss made many attempts to show that random quantities, and
in particular errors in measurement, had to be normally
distributed, His mathematical theorems are correct, but the
physical assumptions fail. One of the greatest errors made
in using statistics is the conversion of data to normality.
However, his discovery of the essential part of what became
the Gauss-Markov Theorem shows that least squares is good
without normality.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
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