Periodica Mathematica Hungarica

, Volume 71, Issue 1, pp 78–91 | Cite as

More accurate Young, Heinz, and Hölder inequalities for matrices



In this paper we deal with a more precise estimates for the matrix versions of Young, Heinz, and Hölder inequalities. First we give an improvement of the matrix Heinz inequality for the case of the Hilbert–Schmidt norm. Then, we refine matrix Young-type inequalities for the case of Hilbert–Schmidt norm, which hold under certain assumptions on positive semidefinite matrices appearing therein. Finally, we give the refinement and the reverse of the matrix Hölder inequality which holds for every unitarily invariant norm. As applications, we also obtain improvements of some well-known matrix inequalities in a quotient form. Our results are compared with the previously known from the literature.


Young inequality Heinz inequality Hölder inequality  Hilbert–Schmidt norm Unitarily invariant norm  Positive semidefinite matrix 

Mathematics Subject Classification

15A42 15A60 26D20 


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2015

Authors and Affiliations

  1. 1.Faculty of Electrical Engineering and ComputingUniversity of ZagrebZagrebCroatia

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