RT Journal Article T1 Distances on the tropical line determined by two points A1 Puente Muñoz, María Jesús De La AB Let p' and q' be points in R-n. Write p' similar to q' if p' - q' is a multiple of (1,...,1). Two different points p and q in R-n/ similar to 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 L(p, q) is caterpillar. We prove that every vertex in L(p, q) belongs to the tropical linear segment joining p and q. A vertex, denoted pq, closest (w.r.t tropical distance) to p exists in L(p, q). Same for q. The distances between pairs of adjacent vertices in L(p, q) and the distances d(p, pq), d(qp, q) and d(p, q) are certain entries of the matrix vertical bar F vertical bar. In addition, if p and q are generic, then the tree L(p, q) is trivalent. The entries of F are differences (i.e., sum of principal diagonal minus sum of secondary diagonal) of order 2 minors of the first two columns of A. PB Kybernetika SN 0023-5954 YR 2014 FD 2014 LK https://hdl.handle.net/20.500.14352/33696 UL https://hdl.handle.net/20.500.14352/33696 LA eng DS Docta Complutense RD 11 abr 2025