G-reflectors: analogues of Householder transformations in scalar product spaces

被引：25

作者：

Mackey, DS ^{[1
]}

Mackey, N

Tisseur, F

机构：

[1] Western Michigan Univ, Dept Math, Kalamazoo, MI 49008 USA

[2] Univ Manchester, Dept Math, Manchester M13 9PL, Lancs, England

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2004年 / 385卷

基金：

英国工程与自然科学研究理事会;

关键词：

scalar product; bilinear; sesquilinear; orthosymmetric; isotropic; householder transformation; hyperbolic transformation; symmetries; transvections; symplectic; pseudo-unitary; structure-preserving;

D O I：

10.1016/j.laa.2003.07.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We characterize the analogues of Householder transformations in matrix groups associated with scalar products, and precisely delimit their mapping capabilities: given a matrix group G and vectors x, y, necessary and sufficient conditions are derived for the existence of a Householder-like analogue G is an element of G 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. (C) 2003 Elsevier Inc. All rights reserved.

引用

页码：187 / 213

页数：27