# The matrix power means and interpolations

Document Type: Original Article

Authors

Abstract

‎It is well-known that the Heron mean is a linear interpolation between the arithmetic and the geometric means while the matrix power mean $P_t(A,B):= A^{1/2}\left(\frac{I+(A^{-1/2}BA^{-1/2})^t}{2}\right)^{1/t}A^{1/2}$ interpolates between the harmonic‎, ‎the geometric‎, ‎and the arithmetic means‎. ‎In this article‎, ‎we establish several comparisons between the matrix power mean‎, ‎the Heron mean and the Heinz mean‎. ‎Therefore‎, ‎we have a deeper understanding about the distribution of these matrix means‎.

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### History

• Receive Date: 05 January 2018
• Revise Date: 23 February 2018
• Accept Date: 28 February 2018