Automorphisms of certain groups and semigroups of matrices

Michael Alwill, Chi Kwong Li, Christina Maher, Nung Sing Sze

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)

Abstract

Characterizations are given for automorphisms of semigroups of nonnegative matrices including doubly stochastic matrices, row (column) stochastic matrices, positive matrices, and nonnegative monomial matrices. The proofs utilize the structure of the automorphisms of the symmetric group (realized as the group of permutation matrices) and alternating group. Furthermore, for each of the above (semi)groups of matrices, a larger (semi)group of matrices is obtained by relaxing the nonnegativity assumption. Characterizations are also obtained for the automorphisms on the larger (semi)groups and their subgroups (subsemigroups) as well.
Original languageEnglish
Pages (from-to)490-525
Number of pages36
JournalLinear Algebra and Its Applications
Volume412
Issue number2-3
DOIs
Publication statusPublished - 15 Jan 2006
Externally publishedYes

Keywords

  • (Generalized) permutation matrices
  • (Semi)group
  • Automorphism
  • Monomial matrices
  • Positive matrices
  • Stochastic matrices

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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