TL;DR
This paper demonstrates that tropical totally positive matrices can be uniquely represented by canonical weighted planar networks and establishes a unique factorization in terms of elementary Jacobi matrices.
Contribution
It introduces a novel representation of tropical totally positive matrices through canonical planar networks and proves a unique factorization theorem.
Findings
Unique representation of tropical totally positive matrices as transfer matrices.
Establishment of a uniqueness theorem for matrix factorization.
Connection between tropical matrices and weighted planar networks.
Abstract
We show that every tropical totally positive matrix can be uniquely represented as the transfer matrix of a canonical totally connected weighted planar network. We deduce a uniqueness theorem for the factorization of a tropical totally positive in terms of elementary Jacobi matrices.
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