Mackey, D. S. and Mackey, Niloufer and Tissuer, 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 |
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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: | 09 Aug 2006 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | http://eprints.maths.manchester.ac.uk/id/eprint/468 |

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