%0 Journal Article
%T Quasi-Rational Canonical Forms of a Matrix over a Number Field
%A Zhudeng Wang
%A Qing Wang
%A Nan Qin
%J Advances in Linear Algebra & Matrix Theory
%P 1-10
%@ 2165-3348
%D 2018
%I Scientific Research Publishing
%R 10.4236/alamt.2018.81001
%X 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.
%K Matrix
%K Jordan Canonical Form
%K Rational Canonical Form
%K Quasi-Rational Canonical Form
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=81645