Geodesic
The general totally positive matrix completion problem with few unspecified entries
The electronic journal of linear algebra, Tome 7 (2000), pp. 1-20.

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

Summary: For m-by-n partial totally positive matrices with exactly one unspecified entry, the set of positions for that entry that guarantee completability to a totally positive matrix are characterized. They are the positions (i; j), i + j ^ 4 and the positions (i; j), i + j * m + n $\Gamma 2$. In each case, the set of completing entries is an open (and infinite in case i = j = 1 or i = m, j = n) interval. In the process some new structural results about totally positive matrices are developed. In addition, the pairs of positions that guarantee completability in partial totally positive matrices with two unspecified entries are characterized in low dimensions.
Classification : 15A48
Keywords: totally positive matrices, matrix completion problems, partial matrix 
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     title = {The general totally positive matrix completion problem with few unspecified entries},
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Fallat, Shaun M.; Johnson, Charles R.; Smith, Ronald L. The general totally positive matrix completion problem with few unspecified entries. The electronic journal of linear algebra, Tome 7 (2000), pp. 1-20. http://geodesic.mathdoc.fr/item/ELA_2000__7__a13/