The theory of generalized inverses has its roots both on semigroup theory and on matrix and operator theory. In this seminar we will focus on the study of the generalized inverse of von Neumann, group, Drazin and Moore-Penrose in a purely algebraic setting. We will present some recent results dealing with the generalized inverse of certain types of matrices and their properties.
Finally, we will present recent applications.
-  Castro-Gonzalez, N.; Robles, J.; Velez-Cerrada, J.Y.; The group inverse of 2×2 matrices over a ring. Linear Algebra and Appl. 438 (2013), no. 9, 36003609.
-  Patricio, P., Hartwig, R.E.; The (2,2,0) Group Inverse Problem, Applied Mathematics and Computation 217(2) (2010), 516-520.
-  Mary, Xavier; Patricio, Pedro; The group inverse of a product, Linear and Multilinear Algebra 64, No 9, 1776-1784 (2016).
-  Nguyen, Thuc Dinh; Dang, Van H., Quasi-inverse Based Cryptography. Computational Science and Its Applications – ICCSA 2013, Lecture Notes in Computer Science, vol. 7974, 2013, 629-642.
-  Patricio, P.; Puystjens, R.; About the von Neumann regularity of triangular block ma- trices, Linear Algebra and Its Applications, 332-334:485-502, 2001.
-  Patricio, P., Hartwig, R.E.; The (2,2,0) Drazin inverse problem, Linear Algebra and its Applications 437(11) (2012), 2755-2772
-  Sun, Hung-Min, Cryptanalysis of a Public-Key Cryptosystem Based on Generalized Inverses of Matrices. IEEE Communications Letters, vol. 5 (2001), no. 2, 61-63.