Restricted quadratic forms, inertia theorems, and the Schur complement (Q1107601)

Let A be a real \(m\times m\) symmetric matrix, then x \(tAx=Q(x)\) is a quadratic form on a real m-dimensional vector space. The inertia of A is the triple (p,q,r), where p, q, and r are the numbers of positive, negative, and zero eigenvectors of A, respectively. For any subspace S of R m the restriction of Q to S is again a quadratic form. The author proves a number of theorems on the inertia of this restriction, inertia formulas involving the Moore-Penrose inverse of A, inertia formulas for partitioned matrices and for the generalized Schur complement of A.