An Extremal Problem for Positive Definite Matrices

Abstract

A problem studied by Flanders is to minimize the function f(R) = tr (SR + T 1/R) over the set of positive definite matrices R, where S and T are positive semi-definite matrices of rank m. Alternative proofs that may have some intrinsic interest are provided. The proofs explicitly yield the infimum to f(R) . One proof is based on a convexity argument and the other on a sequence of reductions to a univariate problem.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1978
Accession Number
ADA060866

Entities

People

  • I. Olkin
  • Theodore W. Anderson

Organizations

  • Stanford University

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Communities of Interest

  • Materials and Manufacturing Processes

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Fields of Study

  • Mathematics

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  • Mathematical Modeling and Probability Theory.
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