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

DOI: 10.4236/alamt.2018.81001, PP. 1-10

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

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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.

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