Characterization of Matrix $K$-Positivity Preserver for $K=\mathbb{R}^n$ and for Compact Sets $K\subseteq\mathbb{R}^n$

This research paper delves into the mathematical properties of matrices that preserve $K$-positivity, a concept related to the preservation of positivity within a specific mathematical framework. The paper focuses on characterizing these matrices for two specific cases: when $K$ represents the entire real space $\mathbb{R}^n$, and when $K$ is a compact subset of $\mathbb{R}^n$. The study likely involves rigorous mathematical proofs and analysis of matrix properties.