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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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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
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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