Unifying unitary and hyperbolic transformations

In this paper, we describe unified formulas for unitary and hyperbolic reflections and rotations, and show how these unified transformations can be used to compute a Hermitian triangular decomposition R̂HDR̂ of a strongly nonsingular indefinite matrix  given in the form Â=X1HX1+αX2HX2,α=±1. The unification is achieved by the introduction of signature matrices which determine whether the applicable transformations are unitary, hyperbolic, or …