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arXiv · 2410.15717

What is an inductive mean?

Frank Nielsen
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Abstract

An inductive mean is a mean defined as a limit of a convergence sequence of other means. Historically, this notion of inductive means obtained as limits of sequences was pioneered independently by Lagrange and Gauss for defining the arithmetic-geometric mean. In this note, we first explain several generalizations of the scalar geometric mean to symmetric positive-definite matrices, and then present several inductive mean mechanisms for sets of symmetric positive-definite matrices.

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Frank Nielsen. 2024-10-21. What is an inductive mean?. https://doi.org/10.1090/noti2832

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