The inertia of hermitian matrices with a prescribed 2×2 block decomposition
Bryan E. Cain, Eduardo Marques de Sá · Linear and Multilinear Algebra · 1992
Let denote given nonnegative integers, and consider the Hermitian matrices where each Hi =Hi* is ni × ni . We characterize the sets of inertias In each case the possible values of In(H)=(πν*) are characterized by a system of linear inequalities involving π,ν and the given integers.