Abstract
The geometric mean of two positive (definite) matrices has been studied for long and found useful in problems of operator theory, quantum mechanics and electrical engineering. For more than two positive matrices the problem of having an acceptable definition was resolved only recently. Among these the object variously called the Riemannian mean, the Karcher mean, the least squares mean, and the barycentre mean is particularly attractive because of intrinsic connections with Riemannian geometry. This mean has also been adopted for applications in image processing, elasticity and other areas. This article is a broad survey of this topic and also reports on some very recent work that is yet to appear in print.
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Bhatia, R. (2013). The Riemannian Mean of Positive Matrices. In: Nielsen, F., Bhatia, R. (eds) Matrix Information Geometry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30232-9_2
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DOI: https://doi.org/10.1007/978-3-642-30232-9_2
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