Doubly stochastic matrix equations |
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Authors: | Montague J S Plemmons R J |
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Institution: | (1) University of Tennessee, Knoxville, Tennessee, USA |
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Abstract: | It is shown that for real,m x n matricesA andB the system of matrix equationsAX=B, BY=A is solvable forX andY doubly stochastic if and only ifA=BP for some permutation matrixP. This result is then used to derive other equations and to characterize the Green’s relations on the semigroup Ω
n
of alln x n doubly stochastic matrices. The regular matrices in Ω
n
are characterized in several ways by use of the Moore-Penrose generalized inverse. It is shown that a regular matrix in Ω
n
is orthostochastic and that it is unitarily similar to a diagnonal matrix if and only if it belongs to a subgroup of Ω
n
. The paper is concluded with extensions of some of these results to the convex setS
n of alln x n nonnegative matrices having row and column sums at most one.
His research was supported by the N. S. F. Grant GP-15943. |
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Keywords: | |
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