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- W2092679380 abstract "Let x and y be positive vectors in Rn. The set of all n × n nonnegative matrices having x and yT as their right and left Perron eigenvectors is a polyhedral convex cone. A cross section of this cone is the polytope P(x,y) consisting of all n × n nonnegative matrices C such that Cx=x and yTC=yT. The set of doubly stochastic matrices is obtained as a special case when x=y=(1,1,…,1)T. Our purpose is to investigate the structure of P(x,y) and especially its extreme points. This is done by transforming the problem into a symmetric transportation polytope, which contains all n × n nonnegative matrices having the same vector z as their row and column sum vector. Using graph-theoretic methods, we investigate the number of extreme points of this polytope. In particular we study vectors z that yield the maximum number of extreme points." @default.
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- W2092679380 date "1991-05-01" @default.
- W2092679380 modified "2023-10-16" @default.
- W2092679380 title "Perron eigenvectors and the symmetric transportation polytope" @default.
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- W2092679380 doi "https://doi.org/10.1016/0024-3795(91)90165-s" @default.
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