- What is... an inductive mean?,
Notices of the American Mathematical Society 70.11 (2023): 1851-1855. (text with two typographic errors corrected):
An inductive mean is a mean defined as a limit of a convergence sequence of other means like the arithmetic-geometric mean.

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Arithmetic-harmonic mean (AHM) = *inductive mean*

- Positive reals: AHM= geometric mean
- Complex numbers: AHM modulus = geometric mean, AHM argument = arithmetic mean
- Positive-definite matrices, AHM = Riemannian geometric mean (wrt trace metric)

Many ways to generalize scalar to matrix geometric means:

- Log-Euclidean mean (quasi-arithmetic mean) but not operator monotone
- Inductive arithmetic-harmonic mean
- Solution of a matrix equation yielding power means + taking limits

Matrix means and monotone operators: