Abstract
We shall discuss the matrix geometric mean for the positive definite matrices. The set of all $n\times n$ matrices with a suitable inner product will be a Hilbert space, and the matrix geometric mean can be considered as a path between two positive matrices. In this paper, we shall obtain a matrix geometric mean inequality, and as an application of it, a property of Riemannian metric space is given. We also obtain some examples related to our result.
Citation
Masatoshi Ito. Yuki Seo. Takeaki Yamazaki. Masahiro Yanagida. "On a geometric property of positive definite matrices cone." Banach J. Math. Anal. 3 (2) 64 - 76, 2009. https://doi.org/10.15352/bjma/1261086710
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