Doubly constrained totally positive line insertion

Abstract

AbstractIt is shown that in any TP matrix, a line (row or column) with two speci˝ed entries in any positions (and the others appropriately chosen) may be inserted in any position, as long as the two entries are consistent with total positivity. This generalizes an unconstrained result previously proven, and the two may not generally be increased to three or more. Applications are given, and this fact should be useful in other completion problems, as the unconstrained result has been.