Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, Vol. 75, No. 4, pp. 1117-1131, 2025

New representations of $(b, c)$-inverses

Li Fang, Liang Zhao

Received October 2, 2024. Published online November 18, 2025.

Abstract: We investigate how to give new representations of $(b,c)$-inverses in terms of core inverses and Drazin inverses. Various new criteria and representations of $(b,c)$-inverses in terms of core inverses and Drazin inverses are established from a new perspective. Since Moore-Penrose inverses, pseudo-inverses, core inverses, dual core inverses, and Bott-Duffin $(e, f )$-inverses are the special cases of $(b, c)$-inverses, new characterizations involving these generalized inverses are also established as corollaries of our results.

Keywords: $(b,c)$-inverse; core inverse; Drazin inverse

Classification MSC: 15A09, 16E50, 16U80

DOI: 10.21136/CMJ.2025.0409-24

PDF available at: Springer Institute of Mathematics CAS Digital Mathematics Library

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Affiliations: Li Fang, Liang Zhao (corresponding author), School of Microelectronics and Data Science, Anhui University of Technology, 59 Hudong N Rd, Huashan District, Maanshan 243032, P. R. China, e-mail: 1142113627@qq.com, lzhao@ahut.edu.cn

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