Author(s)

Zhudeng Wang^*, Qing Wang, Nan Qin

School of Mathematics and Statistics, Yancheng Teachers University, Yancheng, China.

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.

Matrix, Jordan Canonical Form, Rational Canonical Form, Quasi-Rational Canonical Form

Wang, Z. , Wang, Q. and Qin, N. (2018) Quasi-Rational Canonical Forms of a Matrix over a Number Field. Advances in Linear Algebra & Matrix Theory, 8, 1-10. doi: 10.4236/alamt.2018.81001.