arXiv subjects

Sunil Das

Publications and source records attributed to Sunil Das.

2 recordsLinked to original sources

arXiv2024

Sign pattern matrices associated with cycle graphs that require algebraic positivity

A real matrix is said to be positive if its every entry is positive, and a real square matrix A is algebraically positive if there exists a real polynomial f such that f(A) is a positive matrix. A sign pattern matrix A is said to require a property if all matrices having sign pattern as A have that property. In this paper, we characterize all sign pattern matrices associated with cycle graphs that require algebraic positivity.

math.CO↗

arXiv2021

Sign patterns that allow algebraic positivity

A real square matrix is algebraically positive if there exists a real polynomial $f$ such that $f(A)$ is a positive matrix. In this paper, we give a sufficient condition for a sign pattern matrix to allow algebraic positivity, and give some methods to construct higher-order algebraically positive matrices from some lower-order algebraically positive matrices. We also propose two conjectures related to the problem of allowing algebraic positivity.

math.CO↗