# Matrix power means and the Karcher mean

@article{Lim2012MatrixPM, title={Matrix power means and the Karcher mean}, author={Y. Lim and Mikl{\'o}s P{\'a}lfia}, journal={Journal of Functional Analysis}, year={2012}, volume={262}, pages={1498-1514} }

We define a new family of matrix means {Pt(ω;A)}t∈[−1,1], where ω and A vary over all positive probability vectors in Rn and n-tuples of positive definite matrices resp. Each of these means except t≠0 arises as a unique positive definite solution of a non-linear matrix equation, satisfies all desirable properties of power means of positive real numbers and interpolates between the weighted harmonic and arithmetic means. The main result is that the Karcher mean coincides with the limit of power… Expand

#### 130 Citations

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