A note on the rational canonical form of an endomorphism of a vector space of finite dimension
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A note on the rational canonical form of an endomorphism of a vector space of finite dimension

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A note on the rational canonical form of an endomorphism of a vector space of finite dimension

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Ballester-Bolinches, Adolfo Perfil; Esteban Romero, Ramón Perfil; Pérez Calabuig, Vicent
Aquest document és un/a article, creat/da en: 2018
In this note, we give an easy algorithm to construct the rational canonical form of a square matrix or an endomorphism h of a finite dimensional vector space which does not depend on either the structure theorem for finitely generated modules over principal ideal domains or matrices over the polynomial ring. The algorithm is based on the construction of an element whose minimum polynomial coincides with the minimum polynomial of the endomorphism and on the fact that the h-invariant subspace generated by such an element admits an h-invariant complement. It is also shown that this element can be easily obtained without the factorisation of a polynomial as a product of irreducible polynomials.

    Ballester-Bolinches, Adolfo Esteban Romero, Ramón Pérez Calabuig, Vicent 2018 A note on the rational canonical form of an endomorphism of a vector space of finite dimension Operators And Matrices 12 3 823 836
https://doi.org/10.7153/oam-2018-12-49
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