Add to ORKGThe notions of total positivity and of TPk are generalized to shapes (a generalization of matrices). In particular, the relationship between positivity of contiguous minors and all minors is characterized for general shapes and for certain special types of shapes. This and other ideas are used to address the TPk-completion problem and TPk-completable patterns. In case k = 2, a near characterization of TP2-completable patterns is given. (C) 2011 Elsevier Inc. All rights reserved
AbstractAn n×n real matrix is said to be totally positive if every minor is non-negative. In this pa...
AbstractA real matrix is totally positive if all its minors are nonnegative. In this paper, we chara...
AbstractThough total positivity appears in various branches of mathematics, it is rather unfamiliar ...
The notions of total positivity and of TPk are generalized to shapes (a generalization of matrices...
AbstractThe notions of total positivity and of TPk are generalized to “shapes” (a generalization of ...
The notions of total positivity and of TPk are generalized to “shapes” (a generalization of matrices...
Though some special cases are now understood, the characterization of TP-completable patterns is far...
A matrix is called totally nonnegative (TN) if the determinant of every square submatrix is nonnegat...
Abstract. Every partial TP2 (TP1) matrix with one unspecified entry has a TP2 (TP1) com-pletion. For...
AbstractA sufficient condition for complete positivity of a matrix, in terms of complete positivity ...
In earlier work, the labelled graphs G for which every combinatorially symmetric totally nonnegative...
Here, we define and consider (linear) TP-directions and TP-paths for a totally nonnegative matrix, i...
A matrix is called totally nonnegative (TN) if the determinant of every square submatrix is nonnegat...
Abstract. It is shown that if the connected graph of the specified entries of a combinatorially symm...
We first give a complete list of polynomial conditions on the data for TP (TN) completability of par...
AbstractAn n×n real matrix is said to be totally positive if every minor is non-negative. In this pa...
AbstractA real matrix is totally positive if all its minors are nonnegative. In this paper, we chara...
AbstractThough total positivity appears in various branches of mathematics, it is rather unfamiliar ...
The notions of total positivity and of TPk are generalized to shapes (a generalization of matrices...
AbstractThe notions of total positivity and of TPk are generalized to “shapes” (a generalization of ...
The notions of total positivity and of TPk are generalized to “shapes” (a generalization of matrices...
Though some special cases are now understood, the characterization of TP-completable patterns is far...
A matrix is called totally nonnegative (TN) if the determinant of every square submatrix is nonnegat...
Abstract. Every partial TP2 (TP1) matrix with one unspecified entry has a TP2 (TP1) com-pletion. For...
AbstractA sufficient condition for complete positivity of a matrix, in terms of complete positivity ...
In earlier work, the labelled graphs G for which every combinatorially symmetric totally nonnegative...
Here, we define and consider (linear) TP-directions and TP-paths for a totally nonnegative matrix, i...
A matrix is called totally nonnegative (TN) if the determinant of every square submatrix is nonnegat...
Abstract. It is shown that if the connected graph of the specified entries of a combinatorially symm...
We first give a complete list of polynomial conditions on the data for TP (TN) completability of par...
AbstractAn n×n real matrix is said to be totally positive if every minor is non-negative. In this pa...
AbstractA real matrix is totally positive if all its minors are nonnegative. In this paper, we chara...
AbstractThough total positivity appears in various branches of mathematics, it is rather unfamiliar ...