9 papers · 1 filter
SNT-Rank: Kronecker Products and Euclidean Distance Matrices
Bharat Pratap Chauhan, Projesh Nath Choudhury
Symmetric nonnegative matrix trifactorizations (SN-Trifactorizations) were introduced by Bukovšek-Šmigoc [Linear Algebra Appl. 2023] as a symmetric analogue of nonnegative matrix f…
Semigroup automorphisms of total positivity
Projesh Nath Choudhury, Shaun Fallat, Chi-Kwong Li
Totally positive (TP) and totally nonnegative (TN) matrices connect to analysis, mechanics, and to dual canonical bases in reductive groups, by well-known works of Schoenberg, Gant…
Positivity of GCD tensors and their determinants
Projesh Nath Choudhury, Krushnachandra Panigrahy
Let be an ordered set of distinct positive integers. The th-order -dimensional tensor where $t_{i…
Constructing strictly sign regular matrices of all sizes and sign patterns
Projesh Nath Choudhury, Shivangi Yadav
The class of strictly sign regular (SSR) matrices has been extensively studied by many authors over the past century, notably by Schoenberg, Motzkin, Gantmacher, and Krein. A class…
Sign regular matrices and variation diminution: single-vector tests and characterizations, following Schoenberg, Gantmacher-Krein, and Motzkin
Projesh Nath Choudhury, Shivangi Yadav
Variation diminution (VD) is a fundamental property in total positivity theory, first studied in 1912 by Fekete-Pólya for one-sided Pólya frequency sequences, followed by Schoenber…
Nesbitt and Shapiro Cyclic Sum Inequalities for Positive Definite Matrices
Projesh Nath Choudhury, K. C. Sivakumar
The aim of this note is to show that certain number theoretic inequalities due to Nesbitt and Shapiro have noncommutative counterparts involving positive definite matrices.