Subject: Re: Moore-Penrose Inverse
Date: Fri, 12 Nov 2000 18:54:54 -0500
From: Alex Bogomolny

Here's an answer to your question. It came by the way of a friend of mine, Florian Potra, currently at the University of Maryland. Florian went directly to the source: M.Z. Nashed who edited the book

M. Z . Nashed, editor, Generalized Inverses and Applications, Academic Press, 1976.

All the best,
Alexander Bogomolny


  1. E.H. Moore in 1920 generalized the notion of "inverse" of a matrix to include all matrices. Moore's definition of the generalized inverse of a (rectangular) matrix is equivalent to the existence of a matrix G such that AG and GA are appropriate projectors. Moore was a professor at the University of Chicago and was one of the leading American analysts in the early 1900s. Much of his work remained dormant for a long time since he wrote in an obscure way.
  2. Unaware of Moore's work, Penrose showed in 1955 that there exists a unique matrix B such that ABA = A, BAB = B, AB and BA are Hermitian. In 1956 he published a paper showing that the genaralized inverse he has defined has the least squares property. Moore did not have this. Penrose's only 2 papers on generalized inverses are short and elegant, and are based on his Ph.D. at Sheffield, UK.
  3. Penrose is the well known ROGER PENROSE who has profound contributions to tiling, mathematical physics, and other areas. I recall that he gave the Gibbs' lecture at the AMS a few years ago.
  4. Neither Moore nor Penrose considered generalized inverses of operators on Hilbert space, but Tseng, a Chinese student of Moore and Barnard, considered this in his Ph.D. dissertation at Chicago, 1933.

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