## 2007.17: G-Reflectors: Analogues of Householder Transformations in Scalar Product Spaces

2007.17:
D. Steven Mackey, Niloufer Mackey and Françoise Tisseur
(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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PDF - Registered users only - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader 324 Kb |

DOI: 10.1016/j.laa.2003.07.009

## 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 2000 > 15 Linear and multilinear algebra; matrix theory MSC 2000 > 65 Numerical analysis |

MIMS number: | 2007.17 |

Deposited By: | Miss Louise Stait |

Deposited On: | 22 March 2007 |

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