Tensors of Nonnegative Rank Two

2013/05/02 by Allman, Elizabeth S., Rhodes, John A., Sturmfels, Bernd +1 · 1 citation
#14P10 #15A69 #62H17 #Algebraic Geometry (math.AG) #FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1305.0539

Abstract

A nonnegative tensor has nonnegative rank at most 2 if and only if it is supermodular and has flattening rank at most 2. We prove this result, then explore the semialgebraic geometry of the general Markov model on phylogenetic trees with binary states, and comment on possible extensions to tensors of higher rank.

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