Abstract
In this paper, we consider the geometric mean of min matrices. We establish a closed form for the geometric mean of two positive definite min matrices. We further show that the set of min matrices is geodesically convex in the Cartan–Hadamard manifold of positive definite matrices. We also present monotonic one-parameter families of min matrices.
Funding Statement
The work of Shin was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. RS-2023-NR076790). The work of Choi was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2022R1A5A1033624 and RS2024-00342939).
Citation
Byeong-Chun Shin. Yongdo Lim. Hayoung Choi. "The Geometric Mean of Min Matrices." Taiwanese J. Math. Advance Publication 1 - 17, 2025. https://doi.org/10.11650/tjm/250101
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