A weighted core EP inverse

D. E. FERREYRA; F. E. LEVIS; N. THOME

Burjassot

Workshop; International Workshop on Industrial Mathematics / ICIAM Board Meeting 2017; 2017

Faculty of Mathematics of the Universitat de València

The core EP decomposition has been introduced for square matrices in [PM]. Our purpose is double. On the one hand, we develop a weighted core EP decomposition of a pair of rectangular matrices (A,W). On the other hand, we use the previous factorization in order to introduce a new generalized inverse, namely, the weighted core EP inverse. We study its existence and uniqueness and then we provide matrix equations that this new inverse must satisfy. Finally, we derive a characterization for the weighted core EP inverse. The found results constitute an extension to rectangular matrices of the core inverse studied in [BT] for index 1 matrices and extended in [BT2,MT,PM] for arbitrary index. This work is partially supported by Ministerio de Econom´{i}a y Competitividad of Spain (Grants MTM2013-43678-P and Red de Excelencia MTM2015-68805-REDT),a CONICET´s Posdoctoral Research Fellowship, Universidad Nacional de Río Cuarto (grant PPI 18/C472), and CONICET (grant PIP 112-201501-00433CO).REFERENCES: [BT] O.M. Baksalary, G. Trenkler, Core inverse of matrices, Linear and Multilinear Algebra, 58 (6) (2010) 681-697.[BT2] O.M. Baksalary, G. Trenkler, On a generalized core inverse, Applied Mathematics & Compututation, 236 (2014) 450-457.[MT] S.B. Malik, N. Thome, On a new generalized inverse for matrices of an arbitrary index, Applied Mathematics & Compututation, 226 (2014) 575-580.[PM] K.M. Prasad, K.S. Mohana, Core EP inverse, Linear and Multilinear Algebra, 62 (3) (2014) 792-802.