• Hölder’s inequality for matrices

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      https://www.ias.ac.in/article/fulltext/pram/004/05/0242-0245

    • Keywords

       

      Matrix sums; Hölder’s inequality

    • Abstract

       

      We prove that for arbitraryn×n matricesA1,A2,…,Am and for positive real numbersp1,p2,…,pm withp1−1+p2−1+…+pm/−1=1, the inequality$$|Tr(A_1 A_2 ...A_m )^2 |< \mathop {II}\limits_{k = 1}^m [Tr(A_k^\dag A_k )^{p_k } ]P_k^{ - 1} $$ holds.

    • Author Affiliations

       

      C L Mehta1

      1. Department of Physics, Indian Institute of Technology, New Delhi - 110029
    • Dates

       
  • Pramana – Journal of Physics | News

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      Posted on July 25, 2019

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