Matrix Theory

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


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.


Diagonal Element Matrix Theory Complex Matrice Complex Matrix Hermitian Matrix 
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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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