The eigenstructure and Jordan form of the Fourier transform over fields of characteristic 2 and a generalized Vandermonde-type formula

Barone, Marco; Lima, Juliano B.; Souza, Ricardo M. Campello de

doi:10.1016/j.laa.2015.12.021

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2018

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“…Recently, Radjabalipour [1] studied the symmetrization of the Jordan canonical form, Abo et al [2] and Barone et al [3] discussed the relations between the eigenstructures and Jordan canonical form. Moreover, Li [4] discussed the property of the rational canonical form of a matrix, Liu [5] gave out a constructive proof of existence theorem for rational form, and Radjabalipour [6] investigated the rational canonical form via the splitting field.…”

Section: Introductionmentioning

confidence: 99%

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

Wang¹,

Wang²,

Qin³

2018

ALAMT

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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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