Skip to main content

Some Combinatorially Defined Matrix Classes

  • Chapter
  • First Online:
Combinatorial Matrix Theory

Part of the book series: Advanced Courses in Mathematics - CRM Barcelona ((ACMBIRK))

  • 2220 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 37.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

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

Download citation

Publish with us

Policies and ethics