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Quasi-Rational Canonical Forms of a Matrix over a Number Field
School of Mathematics and Statistics, Yancheng Teachers University, Yancheng, China
School of Mathematics and Statistics, Yancheng Teachers University, Yancheng, China
School of Mathematics and Statistics, Yancheng Teachers University, Yancheng, China
- 1 School of Mathematics and Statistics, Yancheng Teachers University, Yancheng, China
- 2 School of Mathematics and Statistics, Yancheng Teachers University, Yancheng, China
- 3 School of Mathematics and Statistics, Yancheng Teachers University, Yancheng, China
Advances in Linear Algebra & Matrix Theory·Volume 08 (2018)·Pages 1–10·Published 9 January 2018·DOI10.4236/alamt.2018.81001
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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.
KeywordsMatrixJordan Canonical FormRational Canonical FormQuasi-Rational Canonical Form
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