COMPLETING A SYMMETRICAL 2X2 BLOCK MATRIX AND ITS INVERSE

We consider the following completion problems. Suppose nl, nz are nonn egative integers such that n(1) + n(2) = n > 0. Let A(11), A(12), A(21 ), B-22 be matrices with dimensions n(1) x n(1), n(2) x n(2), n(2) x n (1), and n(2) x n(2), respectively. We determine necessary and suffici ent conditions so that there exists an n(2) x n(2) matrix A(22) such t hat [GRAPHICS] and (i) A is nonsingular and symmetric, and B-22 is the lower right block of a partitioning of A(-1); (ii) A is symmetric pos itive definite, and B-22 is the lower right block of a partitioning of A(-1).