Geodesic
Conditions for a totally positive completion in the case of a symmetrically placed cycle
The electronic journal of linear algebra, Tome 22 (2011), pp. 125-137.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In earlier work, the labelled graphs G for which every combinatorially symmetric totally nonnegative matrix, the graph of whose specified entries is G, has a totally nonnegative completion were identified. For other graphs, additional conditions on the specified data must hold. Here, necessary and sufficient conditions on the specified data, when G is a cycle, are given for both the totally nonnegative and the totally positive completion problems.
Classification : 15A48, 15A37
Keywords: totally nonnegative matrices, totally positive matrices, partial matrix, matrix completion problem, cycles 
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     author = {Johnson, Charles R. and Kroschel, Brenda K.},
     title = {Conditions for a totally positive completion in the case of a symmetrically placed cycle},
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Johnson, Charles R.; Kroschel, Brenda K. Conditions for a totally positive completion in the case of a symmetrically placed cycle. The electronic journal of linear algebra, Tome 22 (2011), pp. 125-137. http://geodesic.mathdoc.fr/item/ELA_2011__22__a70/