Quasi-Rational Canonical Forms of a Matrix over a Number Field

• 作者: Nan Qin Qing Wang Zhudeng Wang
• 来源期刊: 线性代数与矩阵理论研究进展(英文)
• 学科: 数学
• 关键词: MATRIX Jordan CANONICAL FORM Rational CANONICAL FORM Quasi-Rational CANONICAL FORM
• 年，卷（期）: 2018,（1）
• 页码范围: 1-10
• 页数: 10页
• 分类号: O1

摘要

A matrix is similar to Jordan canonical form over the complex field and the rational canonical form over a number field, respectively. In this paper, we further study the rational canonical form of a matrix over any number field. We firstly discuss the elementary divisors of a matrix over a number field. Then, we give the quasi-rational canonical forms of a matrix by combining Jordan and the rational canonical forms. Finally, we show that a matrix is similar to its quasi-rational canonical forms over a number field.