7 papers
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.
Multivariate blowup-polynomials of graphs
Projesh Nath Choudhury, Apoorva Khare
In recent joint work (2021), we introduced a novel multivariate polynomial attached to every metric space - in particular, to every finite simple connected graph - and showed i…
Characterizing total positivity: single vector tests via Linear Complementarity, sign non-reversal, and variation diminution
Projesh Nath Choudhury
A matrix is called totally positive (or totally non-negative) of order , denoted by TP_k (or TN_k), if all minors of size at most are positive (or non-negative). These m…
Interval hulls of -matrices and almost -matrices
Projesh Nath Choudhury, M. Rajesh Kannan
We establish a characterization of almost -matrices via a sign non-reversal property. In this we are inspired by the analogous results for -matrices. Next, the interval hull…
Bounds for a solution set of linear complementarity problems over Hilbert spaces
Projesh Nath Choudhury, M. Rajesh Kannan, K. C. Sivakumar
Let be a real Hilbert space. In this short note, using some of the properties of bounded linear operators with closed range defined on , certain bounds for a specific convex…
How to Detect and Construct N-matrices
Projesh Nath Choudhury, Michael J. Tsatsomeros
N-matrices are real matrices all of whose principal minors are negative. We provide (i) an test to detect whether or not a given matrix is an N-matrix, and (ii…