Inner-gMP and gMP-inner inverses

Year 2024, , 1312 - 1325, 15.10.2024

Dunja Stojanovic , Dijana Mosic

https://doi.org/10.15672/hujms.1351762

Cited By: 1

Abstract

Solving some systems of operator equations, new kinds of generalized inverses are introduced. Since these new inverses can be expressed by inner and gMP inverses, they are called inner-gMP and gMP-inner inverses. In this way, the concepts of gMP, 1MP and MP1 inverses are generalized. Various representations and characterizations of inner-gMP and gMP-inner inverses are presented. Using the inner and *gMP inverse, we define the inner-*gMP and *gMP-inner inverses which are new extensions of 1MP, MP1 and *gMP inverses. We apply inner-gMP and gMP-inner inverses as well as inner-*gMP and *gMP-inner inverses to solve several kinds of linear equations. Consequently, we obtain solvability of the normal equation which is connected to the least-squares solution. Numerical examples are given to illustrate our results.

Keywords

inner-MP inverse, gMP inverse, core–EP inverse, generalized Drazin inverse

Supporting Institution

Ministry of Education, Science and Technological Development

Project Number

451-03-47/2023-01/200124, 337-00-93/2023-05/13

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