Inner-gMP and gMP-inner inverses

Year 2024, Early Access, 1 - 14

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

References

• [1] O.M. Baksalary and G. Trenkler, Core inverse of matrices, Linear Multilinear Algebra 58 (6), 681-697, 2010.