TITLE:
Quasi-Rational Canonical Forms of a Matrix over a Number Field
AUTHORS:
Zhudeng Wang, Qing Wang, Nan Qin
KEYWORDS:
Matrix, Jordan Canonical Form, Rational Canonical Form, Quasi-Rational Canonical Form
JOURNAL NAME:
Advances in Linear Algebra & Matrix Theory,
Vol.8 No.1,
January
10,
2018
ABSTRACT: 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.