The cone of copositive matrices plays an important role in the reformulation and approximation of difficult optimization problems. A copositive matrix is a real symmetric matrix A such that x^T*A*x is nonnegative for all real vectors x with nonnegative elements. A vector x with nonnegative elements is called a zero of a copositive matrix A if x^T*A*x = 0. The set of nonzero elements of x is called the support of x. In this talk we consider zeros of copositive matrices whose support is minimal with respect to the relation of inclusion. The set of supports of the minimal zeros of a copositive matrix is a convenient finite combinatorial characteristic of the matrix. We investigate the properties of this characteristic and indicate how it might help in the characterization of the extreme rays of the copositive cone.
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