Completing symplectic matrices

被引：1

作者：

Spiegel, E ^{[1
]}

机构：

[1] Univ Connecticut, Dept Math, Storrs, CT 06269 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2000年 / 312卷 / 1-3期

关键词：

hyperbolic plane; symplectic group; Witt's theorem;

D O I：

10.1016/S0024-3795(00)00081-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let F be a field of characteristic not equal 2, V a non-singular 2n-dimensional symplectic space over F, nu(1), nu(2),..., nu(2n) a basis for V, and Sp(n)(F) the collection of symplectic isometries of V with respect to this basis. We consider the following completion question: If A is any n x n F-matrix, must there be some D is an element of Sp(2n) (F) with D = (A * ) * *) It is shown that for some particular important choices of bases, the answer is yes, but it does not hold in general. (C) 2000 Elsevier Science Inc. All rights reserved.

引用

页码：93 / 100

页数：8