Anti-triangular and anti-m-Hessenberg forms for Hermitian matrices and pencils Original Research Article

Hermitian pencils, i.e., pairs of Hermitian matrices, arise in many applications, such as linear quadratic optimal control or quadratic eigenvalue problems. We derive conditions from which anti-triangular and anti-m-Hessenberg forms for general (including singular) Hermitian pencils can be obtained under unitary equivalence transformations.