In mathematics, specifically linear algebra, a real matrix A is copositive if

${\displaystyle x^{T}Ax\geq 0}$

for every nonnegative vector ${\displaystyle x\geq 0}$. The collection of all copositive matrices is a proper cone; it includes as a subset the collection of real positive-definite matrices.

Copositive matrices find applications in economics, operations research, and statistics.