Fredholm's method to solve a
particular integral equation in 1903, was probably the first written
work on generalized inverses. In 1906, Moore formulated the generalized
inverse of a matrix in an algebraic setting, which was published in
1920, and in the thirties von Neumann used generalized inverses in his
studies of continuous geometries and regular rings. Kaplansky and
Penrose, in 1955, independently showed that the Moore "reciprocal
inverse" could be represented by four equations, now known as
Moore-Penrose equations. A big expansion of this area came in the
fifties, when C.R. Rao and J. Chipman made use of the connection between
generalized inverses, least squares and statistics. Generalized
inverses, as we know them presently, cover a wide range of mathematical
areas, such as matrix theory, operator theory, c*-algebras, semi-groups
or rings. They appear in numerous applications that include areas such
as linear estimation, differential and difference equations, Markov
chains, graphics, cryptography, coding theory, incomplete data recovery
and robotics. The aim of this mini-symposium, is to gather researchers
involved in the study of generalized inverses and to encourage the
exchange of ideas.
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