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The totally positive completion problem

open access: yesLinear Algebra and Its Applications, 2004
An n×n real matrix is said to be totally positive if every minor is non-negative. In this paper, we are interested in totally positive completion problems, that is, does a partial totally positive matrix have a totally positive matrix completion?
Cristina Jordan, Juan R Torregrosa
exaly   +2 more sources

Sums of totally positive matrices

open access: yesLinear Algebra and Its Applications, 2004
It is shown that an arbitrary m×n positive matrix can be written as a sum of at most min{m,n} totally positive matrices, and that this is in general the best possible value for the number of summands.
D D Olesky
exaly   +2 more sources

Efficient Recognition of Totally Nonnegative Matrix Cells

open access: yesFoundations of Computational Mathematics, 2013
The space of m×p totally nonnegative real matrices has a stratification into totally nonnegative cells. The largest such cell is the space of totally positive matrices.
Stéphane Launois, T Lenagan
exaly   +2 more sources

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