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Norm inequalities related to the arithmetic–geometric mean inequalities for positive semidefinite matrices



In this paper, we propose three new matrix versions of the arithmetic–geometric mean inequality for unitarily invariant norms, which stem from the fact that the Heinz mean of two positive real numbers interpolates between the geometric and arithmetic means of these numbers. Related trace inequalities are also presented.


Unitarily invariant norm Hilbert–Schmidt norm Singular value Trace Positive semidefinite matrix Inequality 

Mathematics Subject Classification

Primary 15A60 Secondary 15A18 15A42 47A30 47B15 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Mostafa Hayajneh
    • 1
  • Saja Hayajneh
    • 2
  • Fuad Kittaneh
    • 2
  1. 1.Department of MathematicsYarmouk UniversityIrbidJordan
  2. 2.Department of MathematicsThe University of JordanAmmanJordan

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