Matrix inequalities for the difference between arithmetic mean and harmonic mean

2015/01/20 by Wenshi Liao, Liao, Wenshi, Junliang Wu +1
Computer Science · Mathematics · #26E60 #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Mathematical Inequalities and Applications #Matrix Theory and Algorithms #Primary 15A45 #Secondary 15A60

paper · pdf · doi:10.48550/arxiv.1501.04823

openalex publication_date 2015/01/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Motivated by the refinements and reverses of arithmetic-geometric mean and arithmetic-harmonic mean inequalities for scalars and matrices, in this article, we generalize the scalar and matrix inequalities for the difference between arithmetic mean and harmonic mean. In addition, relevant inequalities for the Hilbert-Schmidt norm and determinant are established.

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