Abstract
In this paper, from the viewpoint of the Ando–Hiai inequality, we make a comparison among three geometric means: The Ando–Li–Mathias geometric mean, the Karcher mean and the chaotic geometric mean of positive definite matrices. Among others, we show complements of the -variable Ando–Hiai inequality for the Ando–Li–Mathias geometric mean by means of the Kantorovich constant.
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