ELA, Volume 10, pp. 106-145, May 2003, abstract.

Structured tools for structured matrices

D. Steven Mackey, Niloufer Mackey, and Francoise Tisseur

An extensive and unified collection of structure-preserving 
transformations is presented and organized for easy reference.
The structures involved arise in the context of a non-degenerate 
bilinear or sesquilinear form on R^n or C^n. A variety of 
transformations belonging to the automorphism groups of these 
forms, that imitate the action of Givens rotations, Householder 
reflectors, and Gauss transformations are constructed. Transformations 
for performing structured scaling actions are also described.
The matrix groups considered in this paper are the complex orthogonal, 
real, complex and conjugate symplectic, real perplectic, real and 
complex pseudo-orthogonal, and pseudo-unitary groups. In addition 
to deriving new transformations, this paper collects and unifies 
existing structure-preserving tools.