Heinz mean - Alchetron, The Free Social Encyclopedia

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

H x ( A , B ) = A x B 1 − x + A 1 − x B x 2 .

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:

A B = H 1 / 2 ( A , B ) < H x ( A , B ) < H 0 ( A , B ) = A + B 2 .

The Heinz mean may also be defined in the same way for positive semidefinite matrices, and satisfies a similar interpolation formula.

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