 Copositive matrix

A real symmetric matrix $A$ is copositive if its quadratic form satisfies $x^{T}Ax\ge 0$ for every $x$ in the nonnegative orthant. Every positive semidefinite matrix and every symmetric nonnegative matrix is copositive, as is their sum. The converse fails for the Horn copositive matrix.

A **copositive matrix** is a special type of matrix that arises in the context of optimization and mathematical programming, particularly in the study of quadratic forms and convexity. A symmetric matrix \( A \) is said to be copositive if for any vector \( x \) in the non-negative orthant \( \mathbb{R}^n_+ \) (i.e.