@article{e3e3823ab9c746e19483d4067da64ca8,
title = "Matrix derivatives and Kronecker products for the core and generalized core inverses",
abstract = "We first discuss the Moore-Penrose, Drazin, core and some generalized core inverses, and then use the matrix differential calculus to newly establish matrix derivatives for some of the important matrix functions involving these generalized inverses. We present the generalized inverses of the Kronecker product of two matrices as well.",
keywords = "Drazin inverse, Generalized core inverse, Kronecker product, Matrix differential calculus, Moore-Penrose inverse",
author = "Shuangzhe Liu and Hongxing Wang and Yonghui Liu and Conan Liu",
note = "Funding Information: We would like to thank the Reviewers and Editors very much for their constructive comments which have enhanced the overall presentation of our work. We are deeply grateful to Oskar Baksalary, Jan Hauke, T{\~o}nu Kollo, Tiefeng Ma, Stephen Pollock, Simo Puntanen, Martin Singull, Michel van de Velden and Dietrich von Rosen for their invaluable communications and encouragement which have contributed to our study of matrix derivatives and generalized inverses. The manuscript was presented in abstract at the 29th international workshop on matrices and statistics, IWMS-2023, held at Link{\"o}ping University, Sweden on 21–23 August 2023. Publisher Copyright: {\textcopyright} 2024 Elsevier Inc.",
year = "2024",
month = jul,
doi = "10.1016/j.jmaa.2024.128128",
language = "English",
volume = "535",
pages = "1--14",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",
number = "1",
}