The Heinz mean of two non-negative real numbers A and B was defined by Bhatia[1] as:

with 0 ≤ x ≤ 1/2.

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 < 1/2:

.

**See also
**

* Mean

* Muirhead's inequality

**References
**

1. ^ R. Bathia, Interpolating the arithmetic-geometric mean inequality and its operator version, Lin. Alg. Appl., Vol. 413, p. 355-363 (2006)

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