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From: radams@khis.com (Robert M. Adams)
Subject: Re: Roger Penrose's fixed ideas
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In article <38u1h7$d77@styx.uwa.edu.au>, wojdylo@uniwa.uwa.edu.au (John
Wojdylo) wrote:

> francis@pangea.Stanford.EDU (Francis Muir) writes:
> 
> # Penrose wrote a brilliantly simple paper on unique generalized matrix
> # inverses, and this was the product of a young, clear mind. Then he 
> # began to take himself and his weirdness a little too seriously and
> # did that stuff on aperiodic tiling; great stuff and entertaining too,
> # but he was beginning to play God. Now he is on the Pop Sci Cultur
> # circuit and it is rather lightweight and less than forrmidable. 
> 
> Seems like they all are, these days.
> 
> 
> # Why bother?
> 
> #                                               Fido
> 
> # who was immensely influenced by Penrose's first stuff.
> 
> 
> jw

  Actually, he wrote TWO brilliantly simple papers on the generalized
inverse matrix before R. Rado showed that an equivalent idea had been
proposed by the American mathematician E. H. Moore in 1920(?).  These
results are presently the best kept secrets in the engineering world.  The
generalized inverse of a matrix is not taught below the graduate level,
and to very few graduates.  Nevertheless, Moore/Penrose's work has
amounted to no less than a revolution in problem solving in statistics,
engineering, and elsewhere.  Imagine what other marvels might have emerged
had Penrose kept to this line of work.

  The exact references, for those who wish to follow up on this  topic, are:

Moore, E. H., Abstract in Bull. Am. Math Soc., 26: 394-395.

Moore, E. H., General Analysis, Part I, from Memoirs of the American
Philosophical Society, 1935.

Penrose, R., "A generalized inverse for matrices," Proc Cambridge
Philosophical Society, 1955, 51: 406-413.

Penrose, R., "On the best approximate solutions of linear matrix
equations," Proc Cambridge Philosophical Society, 1956, 52: 17-19.

Rado, R., "Note on generalized inverses of matrices," Proc Cambridge
Philosophical Society, 1956, 52: 600-601.

  For an excellent treatment of the generalized inverse in statistics, see

Albert, Arthur, Regression and the Moore-Penrose Pseudoinverse, Academic
Press, 1972.

-- 
Robert M. Adams (also at CIS 71214,1553)

Opinions expressed here are personal and are not necessarily those of KHIS.
