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Volume 11
Issue 7
10.3390/math11071732
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Article

Minimal Rank Properties of Outer Inverses with Prescribed Range and Null Space

by
Dijana Mosić
1,
Predrag S. Stanimirović
1,2,* and
Spyridon D. Mourtas
2,3
1
Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia
2
Laboratory “Hybrid Methods of Modelling and Optimization in Complex Systems”, Siberian Federal University, Prosp. Svobodny 79, 660041 Krasnoyarsk, Russia
3
Department of Economics, Mathematics-Informatics and Statistics-Econometrics, National and Kapodistrian University of Athens, Sofokleous 1 Street, 10559 Athens, Greece
*
Author to whom correspondence should be addressed.
Mathematics 2023, 11(7), 1732; https://doi.org/10.3390/math11071732
Submission received: 21 February 2023 / Revised: 28 March 2023 / Accepted: 4 April 2023 / Published: 5 April 2023
(This article belongs to the Special Issue Numerical Analysis: Inverse Problems – Theory and Applications)
Versions Notes

Abstract

The purpose of this paper is to investigate solvability of systems of constrained matrix equations in the form of constrained minimization problems. The main novelty of this paper is the unification of solutions of considered matrix equations with corresponding minimization problems. For a particular case we extend some well-known results and give several new results for the weak Drazin inverse. The main characterizations of the Drazin inverse, group inverse and Moore–Penrose inverse are obtained as consequences.
Keywords: matrix equation; generalized inverse; matrix rank matrix equation; generalized inverse; matrix rank

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MDPI and ACS Style

Mosić, D.; Stanimirović, P.S.; Mourtas, S.D. Minimal Rank Properties of Outer Inverses with Prescribed Range and Null Space. Mathematics 2023, 11, 1732. https://doi.org/10.3390/math11071732

AMA Style

Mosić D, Stanimirović PS, Mourtas SD. Minimal Rank Properties of Outer Inverses with Prescribed Range and Null Space. Mathematics. 2023; 11(7):1732. https://doi.org/10.3390/math11071732

Chicago/Turabian Style

Mosić, Dijana, Predrag S. Stanimirović, and Spyridon D. Mourtas. 2023. "Minimal Rank Properties of Outer Inverses with Prescribed Range and Null Space" Mathematics 11, no. 7: 1732. https://doi.org/10.3390/math11071732

APA Style

Mosić, D., Stanimirović, P. S., & Mourtas, S. D. (2023). Minimal Rank Properties of Outer Inverses with Prescribed Range and Null Space. Mathematics, 11(7), 1732. https://doi.org/10.3390/math11071732

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