A Generalization of the Inertia Theorem
Chi‐Tsong Chen · SIAM Journal on Applied Mathematics · 1973
It is shown that the inertia of an $n \times n$ matrix A is equal to the inertia of a Hermitian matrix M if the matrix N given by $N = AM + MA * $ has the property that N is positive semidefinite and the rank of $[ {N\,AN \cdots A^{n - 1} N} ]$ is n. This is a generalization of the result given by Taussky [7] and Ostrowski and Schneider [5].