The semigroup of doubly-stochastic matrices
- 1 January 1966
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Glasgow Mathematical Association
- Vol. 7 (4) , 178-183
- https://doi.org/10.1017/s2040618500035401
Abstract
The set Dn of all n × n doubly-stochastic matrices is a semigroup with respect to ordinary matrix multiplication. This note is concerned with the determination of the maximal subgroups of Dn. It is shown that the number of subgroups is finite, that each subgroup is finite and is in fact isomorphic to a direct product of symmetric groups. These results are applied in § 3 to yield information about the least number of permutation matrices whose convex hull contains a given doubly-stochastic matrix.Keywords
This publication has 7 references indexed in Scilit:
- Spectral properties of doubly-stochastic matricesMonatshefte für Mathematik, 1965
- Results and problems in the theory of doubly-stochastic matricesProbability Theory and Related Fields, 1963
- Some results on non-negative matricesJournal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics, 1961
- Permutation endomorphisms and refinement of a theorem of BirkhoffMathematical Proceedings of the Cambridge Philosophical Society, 1960
- Group membership in rings of various typesMathematische Zeitschrift, 1958
- ConvexityPublished by Cambridge University Press (CUP) ,1958
- Unzerlegbare, nicht negative MatrizenMathematische Zeitschrift, 1950