Congruence of symmetric matrices over local rings

被引：2

作者：

Cao, Yonglin ^{[2
]}

Szechtman, Fernando ^{[1
]}

机构：

[1] Univ Regina, Dept Math & Stat, Saskatoon, SK, Canada

[2] Shandong Univ Technol, Inst Appl Math, Sch Sci, Zibo 255091, Shandong, Peoples R China

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2009年 / 431卷 / 09期

关键词：

Matrix congruence; Bilinear form; Local ring; Principal ideal ring; FORMS;

D O I：

10.1016/j.laa.2009.06.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let R be a commutative, local, and principal ideal ring with maximal ideal in and residue class field F. Suppose that every element of 1 + m is square. Then the problem of classifying arbitrary symmetric matrices over R by congruence naturally reduces, and is actually equivalent to, the problem of classifying invertible symmetric matrices over F by congruence. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：1687 / 1690

页数：4

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