Some Combinatorially Defined Matrix Classes

  • Richard A. Brualdi
Part of the Advanced Courses in Mathematics - CRM Barcelona book series (ACMBIRK)


In this section we consider the symmetric group of permutations of a finite set and their partial order known as the Bruhat order. Regarding a permutation as a permutation matrix, this partial order is related to Gaussian elimination and leads to the matrix Bruhat decomposition of a nonsingular matrix, and then to a characterization of ags in a vector space. We also describe a correspondence between permutations that are involutions (symmetric permutation matrices) and a certain class of nonnegative integral matrices.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Richard A. Brualdi
    • 1
  1. 1.Mathematics DepartmentUniversity of WisconsinMadisonUSA

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