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Matrix Monotone Functions and Convexity

  • Fumio HiaiEmail author
  • Dénes Petz
Chapter
Part of the Universitext book series (UTX)

Abstract

Let \((a, b) \subset {\mathbb R}\) be an interval. A function \(f: (a, b) \rightarrow {\mathbb R}\) is said to be monotone for \(n \times n\) matrices if \(f(A) \le f(B)\) whenever \(A\) and \(B\) are self-adjoint \(n \times n\) matrices, \(A \le B\) and their eigenvalues are in \((a, b)\). If a function is monotone for every matrix size, then it is called matrix monotone or operator monotone.

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© Hindustan Book Agency 2014

Authors and Affiliations

  1. 1.Graduate School of Information SciencesTohoku UniversitySendaiJapan
  2. 2.Alfréd Rényi Institute of MathematicsBudapestHungary
  3. 3.Department for Mathematical AnalysisBudapest University of Technology and EconomicsBudapestHungary

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