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
Full text available as:
 | 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 |
|---|---|
| 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 |
Download Statistics: last 4 weeks
Repository Staff Only: edit this item