Abstract
Recently, a new Riemannian metric and a least squares mean of positive definite matrices have been introduced. They are called the Bures–Wasserstein metric and Wasserstein mean, which are different from the Riemannian trace metric and Karcher mean. In this paper we find relationships of the Wasserstein mean with other matrix means such as the power means, harmonic mean, and Karcher mean.
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Acknowledgements
The work of S. Kim was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIT) (No. NRF-2018R1C1B6001394). The work of H. Lee was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MIST) (No. NRF-2018R1D1A1B07049948).
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Communicated by Takeaki Yamazaki.
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Kim, S., Lee, H. Inequalities of the Wasserstein mean with other matrix means. Ann. Funct. Anal. 11, 194–207 (2020). https://doi.org/10.1007/s43034-019-00025-0
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DOI: https://doi.org/10.1007/s43034-019-00025-0