Heinz mean

In mathematics, the Heinz mean (named after E. Heinz) of two non-negative real numbers A and B, was defined by Bhatia as: In mathematics, the Heinz mean (named after E. Heinz) of two non-negative real numbers A and B, was defined by Bhatia 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: The Heinz mean may also be defined in the same way for positive semidefinite matrices, and satisfies a similar interpolation formula.