Generalized doubly stochastic matrices and linear preservers
A real or complex n×n matrix is generalized doubly stochastic if all of its row sums and column sums equal one. Denote by the linear space spanned by such matrices. We study the reducibility of under the group Γ of linear operators of the form A↦PAQ, where P and Q are n×n permutation matrices. Using...
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| Published in | Linear & multilinear algebra Vol. 53; no. 1; pp. 1 - 11 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Taylor & Francis Group
01.01.2005
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0308-1087 1563-5139 |
| DOI | 10.1080/03081080410001681599 |
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| Abstract | A real or complex n×n matrix is generalized doubly stochastic if all of its row sums and column sums equal one. Denote by
the linear space spanned by such matrices. We study the reducibility of
under the group Γ of linear operators of the form A↦PAQ, where P and Q are n×n permutation matrices. Using this result, we show that every linear operator
mapping the set of generalized doubly stochastic matrices into itself is a linear combination of the operators in Γ followed by a translation of a fixed matrix in
. We compare our results with those from related studies by Sinkhorn and Benson. We also consider similar problems for the generalized symmetric doubly stochastic matrices. |
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| AbstractList | A real or complex n×n matrix is generalized doubly stochastic if all of its row sums and column sums equal one. Denote by
the linear space spanned by such matrices. We study the reducibility of
under the group Γ of linear operators of the form A↦PAQ, where P and Q are n×n permutation matrices. Using this result, we show that every linear operator
mapping the set of generalized doubly stochastic matrices into itself is a linear combination of the operators in Γ followed by a translation of a fixed matrix in
. We compare our results with those from related studies by Sinkhorn and Benson. We also consider similar problems for the generalized symmetric doubly stochastic matrices. |
| Author | Chiang †, Hanley Li, Chi-Kwong |
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| Cites_doi | 10.1016/S0024-3795(00)00242-1 10.1016/S0024-3795(01)00414-1 10.1090/S0002-9939-1971-0269678-1 10.1017/S0004972700037618 10.1080/03081087808817224 |
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| References | bib5 bib6 Chiang H (bib3) 2003; 68 bib4 bib1 bib2 van der Waerden BL (bib7) 1991 |
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| Snippet | A real or complex n×n matrix is generalized doubly stochastic if all of its row sums and column sums equal one. Denote by
the linear space spanned by such... |
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| SubjectTerms | AMS Subject Classifications: 15A04 Linear maps Permutation matrices Symmetric doubly stochastic matrices |
| Title | Generalized doubly stochastic matrices and linear preservers |
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