Conditions for a totally positive completion in the case of a symmetrically placed cycle. (English) Zbl 1226.05157
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.
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.
MSC:
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
| 05C38 | Paths and cycles |
| 15B48 | Positive matrices and their generalizations; cones of matrices |
| 15A83 | Matrix completion problems |
