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Matrix Theory

  • Albert W. Marshall
  • Ingram Olkin
  • Barry C. Arnold
Chapter
Part of the Springer Series in Statistics book series (SSS)

Abstract

The pioneering work of Issai Schur (1923) on majorization was 1 motivated by his discovery that the eigenvalues of a positive semidefi- 2 nite Hermitian matrix majorize the diagonal elements. This discovery 3 provided a new and fundamental understanding of Hadamard’s deter- 4 minant inequality that led Schur to a remarkable variety of related 5 inequalities. Since Schur’s discovery, a number of other majorizations 6 have been found in the context of matrix theory. These majorizations 7 primarily involve quantities such as the eigenvalues or singular val- 8 ues of matrix sums or products. An integral part of the development 9 of majorization in matrix theory is the extremal representations of 10 Chapter 20.

Keywords

Diagonal Element Matrix Theory Complex Matrice Complex Matrix Hermitian Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Albert W. Marshall
    • 1
    • 2
  • Ingram Olkin
    • 3
  • Barry C. Arnold
    • 4
  1. 1.Department of StatisticsUniversity of British ColumbiaVancouverCanada
  2. 2.Lummi IslandUSA
  3. 3.Department of StatisticsStanford UniversityStanfordUSA
  4. 4.Department of StatisticsUniversity of CaliforniaRiversideUSA

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