Invariance of Total Positivity of a Matrix under Entry-wise Perturbation and Completion Problems

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In: A Panorama of Mathematics: Pure and Applied, Contemporary Mathematics, vol. 658, Amer. Math. Soc.,

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A totally positive matrix is a matrix having all its minors positive. The largest amount by which the single entries of such a matrix can be perturbed without losing the property of total positivity is given. Also some completion problems for totally positive matrices are investigated.

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