In mathematics, the Heinz mean (named after E. Heinz) of two non-negative real numbers ''A'' and ''B'', was defined by Bhatia as: :

\operatorname_x(A, B) = \frac,

with 0 ≤ ''x'' ≤ . For different values of ''x'', this Heinz mean interpolates between the

arithmetic Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th ...

(''x'' = 0) and

geometric Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ca ...

(''x'' = 1/2) means such that for 0 < ''x'' < : :

\sqrt = \operatorname_\frac(A, B) < \operatorname_x(A, B) < \operatorname_0(A, B) = \frac.

The Heinz means appear naturally when symmetrizing

\alpha

-divergences. It may also be defined in the same way for positive semidefinite matrices, and satisfies a similar interpolation formula..

References

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See also

References