scholarly journals Sign non‐reversal property for totally non‐negative and totally positive matrices, and testing total positivity of their interval hull

2021 ◽  
Author(s):  
Projesh Nath Choudhury ◽  
M. Rajesh Kannan ◽  
Apoorva Khare
Keyword(s):  
Total Positivity ◽  
Totally Positive ◽  
Positive Matrices ◽  
Interval Hull ◽  
Totally Positive Matrices

Introduction

2011 ◽  
Author(s):  
Shaun M. Fallat ◽  
Charles R. Johnson
Keyword(s):  
Total Positivity ◽  
Nonnegative Matrices ◽  
Extant Literature ◽  
Totally Positive ◽  
Positive Matrices ◽  
Class Of Matrices ◽  
Totally Positive Matrices

This introductory chapter is an overview of totally positive (or nonnegative) matrices (TP or TN matrices). Positivity has roots in every aspect of pure, applied, and numerical mathematics. The subdiscipline, total positivity, also is entrenched in nearly all facets of mathematics. At first it may appear that the notion of total positivity is artificial; however, this class of matrices arises in a variety of important applications. Historically, the theory of totally positive matrices originated from the pioneering work of Gantmacher and Krein in 1960. The chapter explores the extant literature on total positivity since then, before proceeding to the definitions and notations to be used in the rest of this volume. It also provides a brief overview of the succeeding chapters.

Some Conjectures for Immanants

1992 ◽  
Vol 44 (5) ◽  
pp. 1079-1099 ◽  
Author(s):  
J. R. Stembridge
Keyword(s):  
Total Positivity ◽  
Supporting Evidence ◽  
Combinatorial Structures ◽  
The Third ◽  
Totally Positive ◽  
Positive Matrices ◽  
Nonnegative Coefficients ◽  
Totally Positive Matrices ◽  
Real Matrices

AbstractWe present a series of conjectures for immanants, together with the supporting evidence we possess for them. The conjectures are loosely organized into three families. The first concerns inequalities involving the immanants of totally positive matrices (Le.,real matrices with nonnegative minors). This includes, for example, the conjecture that immanants of totally positive matrices are nonnegative. The second family involves the immanants of Jacobi-Trudi matrices. These conjectures were suggested by a previous conjecture of Goulden and Jackson (recently proved by C. Greene) that the immanants of Jacobi-Trudi matrices are polynomials with nonnegative coefficients. The third family involves geometric and combinatorial structures associated with total positivity and paths in acyclic digraphs.

scholarly journals Generalized even and odd totally positive matrices

2011 ◽  
Vol 435 (11) ◽  
pp. 2722-2730
Author(s):  
O.Y. Kushel ◽  
P. Sharma
Keyword(s):  
Totally Positive ◽  
Positive Matrices ◽  
Totally Positive Matrices

scholarly journals Sequence Characterization of 3-Dimensional Riordan Arrays and Some Application

2019 ◽  
Vol 74 (4) ◽  
Author(s):  
Roksana Słowik
Keyword(s):  
Sequence Characterization ◽  
3 Dimensional ◽  
Riordan Arrays ◽  
Totally Positive ◽  
Positive Matrices ◽  
Totally Positive Matrices

Abstract We propose the characterization of 3-dimensional Riordan arrays with use of three sequences that is analogous to the representation of 2-dimensional Riordan arrays with use of A and Z-sequence. We also suggest an application of this representation for finding totally positive matrices.

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