Bounds for the completely positive rank of a symmetric matrix over a tropical semiring

David Dol\v{z}an; Polona Oblak

arxiv: 1705.02117 · v2 · pith:37VZJSSRnew · submitted 2017-05-05 · 🧮 math.RA

Bounds for the completely positive rank of a symmetric matrix over a tropical semiring

David Dol\v{z}an , Polona Oblak This is my paper

classification 🧮 math.RA

keywords matrixgraphsemiringtropicalaccordingbegetboundbounds

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In this paper, we find an upper bound for the CP-rank of a matrix over a tropical semiring, according to the vertex clique cover of the graph prescribed by the pattern of the matrix. We study the graphs that beget the patterns of matrices with the lowest possible CP-ranks and prove that any such graph must have its diameter equal to 2.

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Bounds for the completely positive rank of a symmetric matrix over a tropical semiring

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