Automorphisms of certain groups and semigroups of matrices

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

doi:10.1016/j.laa.2005.07.015

Automorphisms of certain groups and semigroups of matrices

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

Research output: Journal article publication › Journal article › Academic research › peer-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 language	English
Pages (from-to)	490-525
Number of pages	36
Journal	Linear Algebra and Its Applications
Volume	412
Issue number	2-3
DOIs	https://doi.org/10.1016/j.laa.2005.07.015
Publication status	Published - 15 Jan 2006
Externally published	Yes

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

More information

10.1016/j.laa.2005.07.015

Cite this

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title = "Automorphisms of certain groups and semigroups of matrices",

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.",

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author = "Michael Alwill and Li, {Chi Kwong} and Christina Maher and Sze, {Nung Sing}",

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T1 - Automorphisms of certain groups and semigroups of matrices

AU - Alwill, Michael

AU - Li, Chi Kwong

AU - Maher, Christina

AU - Sze, Nung Sing

PY - 2006/1/15

Y1 - 2006/1/15

N2 - 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.

AB - 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.

KW - (Generalized) permutation matrices

KW - (Semi)group

KW - Automorphism

KW - Monomial matrices

KW - Positive matrices

KW - Stochastic matrices

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U2 - 10.1016/j.laa.2005.07.015

DO - 10.1016/j.laa.2005.07.015

M3 - Journal article

SN - 0024-3795

VL - 412

SP - 490

EP - 525

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 2-3

ER -

Automorphisms of certain groups and semigroups of matrices

Abstract

Keywords

ASJC Scopus subject areas

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