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arXiv · 2112.00442

Sign patterns that allow algebraic positivity

Sunil Das
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Abstract

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.

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Sunil Das. 2022-03-22. Sign patterns that allow algebraic positivity. https://doi.org/10.1016/j.laa.2022.08.007

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