TL;DR
This paper introduces new inequalities related to the harmonic mean for scalars and matrices, utilizing spectral decomposition to refine, reverse, and analyze harmonic matrix perturbations.
Contribution
It presents novel inequalities for harmonic means of matrices, including refinements, reversals, and perturbation bounds, using spectral decomposition techniques.
Findings
New inequalities for harmonic mean of matrices
Refinements and reversals of existing inequalities
Bounds on harmonic matrix perturbations
Abstract
The main goal of this article is to present new types of inequalities refining and reversing inequalities of the harmonic mean of scalars and matrices. Furthermore, implementing the spectral decomposition of positive matrices, we present a new type of inequalities treating certain harmonic matrix perturbation.
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Taxonomy
TopicsMathematical Inequalities and Applications · Matrix Theory and Algorithms · Mathematical functions and polynomials