ELA, Volume 7, pp. 112-151, September 2000, abstract.  

Canonical forms for doubly structured matrices and pencils

Christian Mehl, Volker Mehrmann, and Hongguo Xu

In this paper, canonical forms under structure-preserving 
equivalence transformations are presented for matrices and 
matrix pencils that have a multiple structure, which is 
either an H-self-adjoint or H-skew-adjoint structure, where 
the matrix H is a complex nonsingular Hermitian or skew-
Hermitian matrix.  Matrices and pencils of such multiple 
structures arise, for example, in quantum chemistry in 
Hartree-Fock models or random phase approximation.