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Volume 11
Issue 6
10.3390/axioms11060291
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Article

Characterizations of Matrix Equalities for Generalized Inverses of Matrix Products

by
Yongge Tian
Shanghai Business School, College of Business and Economics, Shanghai 201499, China
Axioms 2022, 11(6), 291; https://doi.org/10.3390/axioms11060291
Submission received: 3 May 2022 / Revised: 29 May 2022 / Accepted: 7 June 2022 / Published: 14 June 2022
Versions Notes

Abstract

This paper considers how to construct and describe matrix equalities that are composed of algebraic operations of matrices and their generalized inverses. We select a group of known and new reverse-order laws for generalized inverses of several matrix products and derive various necessary and sufficient conditions for them to hold using the matrix rank method and the block matrix method.
Keywords: generalized inverse; matrix product; matrix equality; reverse-order law; set inclusion; rank; range; block matrix generalized inverse; matrix product; matrix equality; reverse-order law; set inclusion; rank; range; block matrix

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MDPI and ACS Style

Tian, Y. Characterizations of Matrix Equalities for Generalized Inverses of Matrix Products. Axioms 2022, 11, 291. https://doi.org/10.3390/axioms11060291

AMA Style

Tian Y. Characterizations of Matrix Equalities for Generalized Inverses of Matrix Products. Axioms. 2022; 11(6):291. https://doi.org/10.3390/axioms11060291

Chicago/Turabian Style

Tian, Yongge. 2022. "Characterizations of Matrix Equalities for Generalized Inverses of Matrix Products" Axioms 11, no. 6: 291. https://doi.org/10.3390/axioms11060291

APA Style

Tian, Y. (2022). Characterizations of Matrix Equalities for Generalized Inverses of Matrix Products. Axioms, 11(6), 291. https://doi.org/10.3390/axioms11060291

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