In mathematics, the Heinz mean (named after E. HeinzE. Heinz (1951), "Beiträge zur Störungstheorie der Spektralzerlegung", Math. Ann., 123, pp. 415–438.) of two non-negative real numbers A and B, was defined by Bhatia. as:
with 0 ≤ x ≤ .
For different values of x, this Heinz mean interpolates between the arithmetic (x = 0) and geometric (x = 1/2) means such that for 0 < x < :
The Heinz means appear naturally when symmetrizing -divergences..
It may also be defined in the same way for positive semidefinite matrices, and satisfies a similar interpolation formula...
See also Mean Muirhead's inequality Inequality of arithmetic and geometric means
References