## MAP-PDMA

**Pedro Patrício**

*CMAT - University of Minho*

**Abstract ::** 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.

In this seminar we will focus on the study of the generalized inverse of von Neumann, group, outer and Moore-Penrose in a purely algebraic setting and matrix setting. We will present some recent results dealing with the generalized inverse of certain types of matrices over rings, emphasizing the proof techniques used.

We will address some applications.

Seminar Room of DMat-UMinho (3.08), and via zoom at

https://videoconf-colibri.zoom.us/j/92403741454?pwd=UE43T1c3M3g5Y3VoWlZENkMwaGcrUT09

Seminar for the Doctoral Program in Applied Mathematics (MAP-PDMA Seminar)