Article citationsMore>>

Liu, X.Z. (2006) A Constructive Proof of Existence Theorem for Rational Form. College Mathematics, 22, 125-128. (In Chinese)

has been cited by the following article:

• 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.