Analyticity of the Karcher mean coefficient maps
The main concern of this paper is the three-variable Karcher (alternatively, Riemannian or Cartan) matrix mean for 2×2 linearly independent triples of positive definite matrices. We show that such triples form an analytic manifold and obtain three analytic functions from (1,∞)2×(0,π/2) to (0,1) realizing the Karcher mean as a linear combination of variables.
Publication Source (Journal or Book title)
Linear Algebra and Its Applications
Lawson, J., & Lim, Y. (2021). Analyticity of the Karcher mean coefficient maps. Linear Algebra and Its Applications, 627, 162-184. https://doi.org/10.1016/j.laa.2021.06.009