Revisiting Some Relationships Between the Weighted Spectral Mean and the Wasserstein Mean

Minh Thanh Duong (), Anh Vu Le, Cong Trinh Le and Trung Hoa Dinh
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Minh Thanh Duong: Department of Primary Education, Ho Chi Minh City University of Education, Ho Chi Minh City 700000, Vietnam
Anh Vu Le: Department of Economic Mathematics, University of Economics and Law, Ho Chi Minh City, Vietnam and Vietnam National University, Ho Chi Minh City 700000, Vietnam
Cong Trinh Le: Department of Mathematics and Statistics, Quy Nhon University, Quy Nhon 55100, Vietnam
Trung Hoa Dinh: Department of Mathematics and Statistics, Troy University, Troy, AL 36082, USA

Mathematics, 2025, vol. 13, issue 10, 1-10

Abstract: In this paper, we introduce the 2-geometric mean and explore its connections with the spectral geometric mean and the Wasserstein mean for positive definite matrices. Additionally, we revisit and establish several inequalities involving these means in the context of the near order relation.

Keywords: spectral geometric mean; geometric mean; Wasserstein mean; Riccati equation; central elements (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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