G-Reflectors in Scalar Product Spaces∗
نویسندگان
چکیده
We characterize the analogues of Householder reflectors in matrix groups associated with scalar products. Examples of such groups include the symplectic and pseudounitary groups. We also precisely delimit the mapping capabilities of these Householder analogues: given a matrix group G and vectors x, y, we give necessary and sufficient conditions for the existence of a Householder-like analogue G ∈ G such that Gx = y. When G exists, we show how it can be constructed from x and y.
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