G-Reflectors: Analogues of Householder Transformations in Scalar Product Spaces

Mackey, D. Steven and Mackey, Niloufer and Tisseur, Françoise (2004) G-Reflectors: Analogues of Householder Transformations in Scalar Product Spaces. Linear Algebra and its Applications, 385. pp. 187-213. ISSN 0024-3795

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Abstract

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.

Item Type:	Article
Uncontrolled Keywords:	Scalar product; Bilinear; Sesquilinear; Orthosymmetric; Isotropic; Householder transformation; Hyperbolic transformation; Symmetries; Transvections; Symplectic; Pseudo-unitary; Structure-preserving
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User:	Ms Lucy van Russelt
Date Deposited:	22 Mar 2007
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/720

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