double struct G sign-reflectors: Analogues of Householder transformations in scalar product spaces

We characterize the analogues of Householder transformations in matrix groups associated with scalar products, and precisely delimit their mapping capabilities: given a matrix group G and vectors x, y, necessary and sufficient conditions are derived for the existence of a Householder-like analogue G∈double struct G sign such that Gx=y. When G exists, we show how it can be constructed from x and y. Examples of matrix groups to which these results apply include the symplectic and pseudo-unitary groups. © 2003 Elsevier Inc. All rights reserved.