Haynsworth inertia additivity formula
In mathematics, the Haynsworth inertia additivity formula, discovered by Emilie Virginia Haynsworth, concerns the number of positive, negative, and zero eigenvalues of a Hermitian matrix and of block matrices into which it is partitioned.
The inertia of a Hermitian matrix H is defined as the ordered triple
whose components are respectively the numbers of positive, negative, and zero eigenvalues of H. Haynsworth considered a partitioned Hermitian matrix
where H11 is nonsingular and H12* is the conjugate transpose of H12. The formula states:
where H/H11 is the Schur complement of H11 in H:
