Pedro Patrício

CMAT-UM

pedro@math.uminho.pt

October 15, 2019

In 1906, Moore formulated the generalized inverse of a matrix in an algebraic setting, which was published in 1920. Kaplansky and Penrose, in 1955, independently showed that the Moore “reciprocal inverse” could be represented by four equations, now known as Moore-Penrose equations. 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. We will address some of these applications.