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Summer 2018 The matrix power means and interpolations
Trung Hoa Dinh, ‎Raluca Dumitru, Jose A‎. ‎Franco
Adv. Oper. Theory 3(3): 647-654 (Summer 2018). DOI: 10.15352/aot.1801-1288

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.

Citation

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Trung Hoa Dinh. ‎Raluca Dumitru. Jose A‎. ‎Franco. "The matrix power means and interpolations." Adv. Oper. Theory 3 (3) 647 - 654, Summer 2018. https://doi.org/10.15352/aot.1801-1288

Information

Received: 5 January 2018; Accepted: 28 February 2018; Published: Summer 2018
First available in Project Euclid: 4 April 2018

zbMATH: 06902458
MathSciNet: MR3795106
Digital Object Identifier: 10.15352/aot.1801-1288

Subjects:
Primary: 47A63
Secondary: 47A56 , 47A64

Keywords: arithmetic mean , geometric mean , harmonic mean , ‎Heinz means , ‎Heron means , interpolation , Kubo-Ando means , ‎power means

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.3 • No. 3 • Summer 2018
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