摘要: It is shown that any two-variable-mean of positive matrices (studied by Kubo and Ando) can be extended to more variables. The $n$-variable-mean $M_n(A_1,A_2,\ldots,A_n)$ defined a symmetrization procedure when the $n$-tuple $(A_1, A_2, \ldots, A_n)$ ordered, monotone in each variable, satisfies transformer inequality. This approach motivated paper Ando, Li, Mathias on geometric means [Linear Algebra Appl., 385 (2004), pp. 305-334]. Special attention paid logarithmic mean. conjectured for matrix converges all triplets.
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