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Intervals of Totally Nonnegative and Related Matrices

✍ Scribed by J. Garloff

Publisher
John Wiley and Sons
Year
2002
Weight
93 KB
Volume
1
Category
Article
ISSN
1617-7061

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✦ Synopsis

Intervals of Totally Nonnegative and Related Matrices

We consider the class of the totally nonnegative matrices, i.e., the matrices having all their minors nonnegative, and intervals of matrices with respect to the chequerboard partial ordering, which results from the usual entrywise partial ordering if we reverse the inequality sign in all components having odd index sum. For these intervals we study the following conjecture: If the left and right endpoints of an interval are nonsingular and totally nonnegative then all matrices taken from the interval are nonsingular and totally nonnegative. We present a new class of the totally nonnegative matrices for which this conjecture holds true. Similar results for classes of related matrices are also given.

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