Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 3, Number 2 (2009), 64-76.
On a geometric property of positive definite matrices cone
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.
Banach J. Math. Anal. Volume 3, Number 2 (2009), 64-76.
First available in Project Euclid: 17 December 2009
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Ito, Masatoshi; Seo, Yuki; Yamazaki, Takeaki; Yanagida, Masahiro. On a geometric property of positive definite matrices cone. Banach J. Math. Anal. 3 (2009), no. 2, 64--76. doi:10.15352/bjma/1261086710. https://projecteuclid.org/euclid.bjma/1261086710