image-reflectors: analogues of Householder transformations in scalar product spaces Original Research Article

We characterize the analogues of Householder transformations in matrix groups associated with scalar products, and precisely delimit their mapping capabilities: given a matrix group image and vectors x, y, necessary and sufficient conditions are derived for the existence of a Householder-like analogue image 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.