Beschreibung
Moore, E.H. And Roger Penrose. Moore-Penrose Inverse--3 papers in 3 bound volumes. "On the reciprocal of the general algebraic matrix" AND WITH "A generalized inverse for matrices" AND WITH "On Best Approximate Solutions of Linear Matrix Equations". The Moore is in Bulletin of the American Math Society and the Penroses are in Proceedings of the Cambridge Philosophical Society. [++] Includes: (1) Moore, E. H. (1920). "On the reciprocal of the general algebraic matrix". Bulletin of the American Mathematical Society. 26 (9): 394 95 in the full volume of 488pp+54pp, including the bound in wrappers for issues 1 and 10. Bound in cloth and marbled boards. Very sturdy. Ex-library, with a few small and tidy stamps on spine and two stamps on the title page. Nice copy. (2) Penrose, Roger (1955). "A generalized inverse for matrices". Proceedings of the Cambridge Philosophical Society. Volume 51 (part 3); pp 406 13, in the volume of 772pp. Bound in cloth, very moderately ex-library (Birkbeck College), a FINE copy. This volume contains the wrappers for each of the four parts bound in at end. [Cited 5,000+ times.] [++] (3) Penrose, Roger (1955). "On Best Approximate Solutions of Linear Matrix Equations" Proceedings of the Cambridge Philosophical Society. Volume 52 (part 1): pp 17-19 in the volume of 772pp. Bound in cloth, very moderately ex-library (Birkbeck College), a FINE copy. This volume contains the wrappers for each of the four parts bound in at end.[Cited nearly 900 times.] [++] "As a mathematical area generalized inversion1 was inaugurated in 1955 by R. Penrose [128]. Since then there have appeared about 2000 articles and 15 books on generalized inverses of matrices and linear operators."--"Generalized inverses of matrices: a perspective of the work of Penrose Mathematical Proceedings of the Cambridge Philosophical Society", A. Ben-Israel, 2008 [++] "In mathematics, and in particular linear algebra, the Moore Penrose inverse of a matrix is the most widely known generalization of the inverse matrix. It was independently described by E. H. Moore in 1920, Arne Bjerhammar in 1951, and Roger Penrose in 1955. [Penrose engaged and reintroduced the Moore while still a student, receiving his Ph.D. In 1958.] Earlier, Erik Ivar Fredholm [whose work on integral equations and operator theory foreshadowed the theory of Hilbert spaces] had introduced the concept of a pseudoinverse of integral operators in 1903. When referring to a matrix, the term pseudoinverse, without further specification, is often used to indicate the Moore Penrose inverse. The term generalized inverse is sometimes used as a synonym for pseudoinverse. A common use of the pseudoinverse is to compute a "best fit" (least squares) solution to a system of linear equations that lacks a solution. Another use is to find the minimum (Euclidean) norm solution to a system of linear equations with multiple solutions. The pseudoinverse facilitates the statement and proof of results in linear algebra. The pseudoinverse is defined and unique for all matrices whose entries are real or complex numbers. It can be computed using the singular value decomposition." [++] See also: Nashed, M. Z. and Rall, L. B. Annotated bibliography on generalized inverses and applications, pp. 771 1041.
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