Matrix Factorizations, Compounds, Direct Products, and M-Matrices

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


It is often convenient to represent a matrix in terms of other matrices that have special properties. Of the many such known representa- tions, a few are listed here that relate to the development of this book. General references for some of the material are Bellman (1960), Householder (1964), and Mirsky (1955a). An exposition of exponential and polar representations of matrices is given by de Bruijn and Szekeres (1955). For a compendium on matrix factorizations, see Bernstein (2005, Chapter 5).


Diagonal Element Matrix Factorization Complex Matrice Triangular Matrix Complex 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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