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Distances on the tropical line determined by two points

María Jesús de la Puente (2014)

Kybernetika

Let p ' and q ' be points in n . Write p ' q ' if p ' - q ' is a multiple of ( 1 , ... , 1 ) . Two different points p and q in n / uniquely determine a tropical line L ( p , q ) passing through them and stable under small perturbations. This line is a balanced unrooted semi-labeled tree on n leaves. It is also a metric graph. If some representatives p ' and q ' of p and q are the first and second columns of some real normal idempotent order n matrix A , we prove that the tree L ( p , q ) is described by a matrix F , easily obtained from A . We also prove that...

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