On a geometric property of positive definite matrices cone
Ito, Masatoshi ; Seo, Yuki ; Yamazaki, Takeaki ; Yanagida, Masahiro
Banach J. Math. Anal., Tome 3 (2009) no. 2, p. 64-76 / Harvested from Project Euclid
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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.
Publié le : 2009-05-15
Classification:  Positive matrix,  Riemannian metric,  geometric mean,  47A64,  47A63,  47L25 
@article{1261086710,
     author = {Ito, Masatoshi and Seo, Yuki and Yamazaki, Takeaki and Yanagida, Masahiro},
     title = {On a geometric property of positive definite matrices cone},
     journal = {Banach J. Math. Anal.},
     volume = {3},
     number = {2},
     year = {2009},
     pages = { 64-76},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1261086710}
}

Ito, Masatoshi; Seo, Yuki; Yamazaki, Takeaki; Yanagida, Masahiro. On a geometric property of positive definite matrices cone. Banach J. Math. Anal., Tome 3 (2009) no. 2, pp.  64-76. http://gdmltest.u-ga.fr/item/1261086710/