Orthosymmetric block reflectors

We develop a general theory of reflectors and block reflectors in a class of non-Euclidean scalar product spaces generated by orthosymmetric scalar product matrices J. These J-reflectors are generalizations of ordinary Householder transformations, and we show that they can always be expressed in a Householder-like representation. Reflection and mapping properties of J-reflectors are completely described. Block J-reflectors can be used for block annihilation in QR-like factorizations, where Q is J-unitary and R is block upper triangular.