Criteria for copositive matrices of order four (Q1318220)

A symmetric matrix \(A\in \mathbb{R}^{n\times n}\) is called (strictly) copositive if \(x^ TAx\geq(>)0\) for all \(x\in \mathbb{R}^ n_ +\). One proves that the (strict) copositivity of \(A\) is equivalent to the (strict) copositivity of two symmetric matrices of order \(n-1\) if \(A\) has a row whose off-diagonal elements are all nonpositive. Criteria for (strictly) copositive matrices of order 3 and 4 are derived.