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Adolfo Ballester-Bolinches, Ramón Esteban-Romero, Vicente Pérez-Calabuig
A note on the rational canonical form of an endomorphism of a vector space of finite dimension
Operators and Matrices, 12 (3):823-836, 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.
2010 Mathematics Subject Classification: 15A21, 12E05, 12Y05
Keywords: Similarity of matrices, rational canonical form, minimum polynomial, endomorphism.