POSITIVE SEMIDEFINITE MATRICES - CHARACTERIZATION VIA CONICAL HULLS AND LEAST-SQUARES SOLUTION OF A MATRIX EQUATION

Any real symmetric n×n matrix A can be described by an n(n+1)/2-component vector. Positive semidefiniteness of A is characterized by the associated vector belonging to the conical hull of a suitable convex set. This characterization is used to facilitate least-squared error solution, with respect to such A, of F=AG, where F and G are given matrices. The solution method involves finding the point in the conical hull of a convex set which is nearest to a vector. An algorithm is given for solving that proximal point problem.