The matrix geometric mean
نویسندگان
چکیده
An attractive candidate for the geometric mean of m positive definite matrices A1, . . . , Am is their Riemannian barycentre G. One of its important properties, monotonicity in the m arguments, has been established recently by J. Lawson and Y. Lim. We give a much simpler proof of this result, and prove some other inequalities. One of these says that, for every unitarily invariant norm, |||G||| is not bigger than the geometric mean of |||A1|||, . . . , |||Am|||. Mathematics Subject Classification (2010): 15B48, 47A64, 53C20
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