Abstract
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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Brualdi, R.A. (2018). Some Combinatorially Defined Matrix Classes. In: Encinas, A., Mitjana, M. (eds) Combinatorial Matrix Theory . Advanced Courses in Mathematics - CRM Barcelona. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-70953-6_1
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DOI: https://doi.org/10.1007/978-3-319-70953-6_1
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-70952-9
Online ISBN: 978-3-319-70953-6
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