2026-06-27T22:29:08Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/648412023-08-25T16:36:45Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense
author
Montesinos Amilibia, José María
2023-06-21T02:05:52Z
2023-06-21T02:05:52Z
1970
0016-3805
https://hdl.handle.net/20.500.14352/64841
http://dmle.cindoc.csic.es/pdf/GACETAMATEMATICA_1970_22_1-2_03.pdf
The author gives a very interesting new equivalence for automorphisms u and u′ of a finite-dimensional vector space E over a field K. He defines u and u′ to be equivalent if there exists another automorphism H of E such that every u-invariant subspace is also H−1u′ H-invariant, and every u′-invariant subspace is also H−1u H-invariant. Suppose now that K contains the sets Q={q1,⋯,qr}, Q′={q1′,⋯,qs′} of roots of the minimal polynomials of u,u′, respectively. The author proves then that u and u′ are equivalent if and only if there exists a bijection λ:Q→Q′ such that the elementary divisor degrees of qi and λ(qi) are identical for i=1,⋯,r=s. For a given space E over an algebraically closed field K, the number of equivalence classes of automorphisms is finite.
The author notes that this equivalence, less fine than similarity, preserves many of the geometric properties of automorphisms. {The reviewer notes that the definition of equivalence can be extended to arbitrary endomorphisms; the results quoted above seem to carry over to the more general case.}
spa
A new classification of automorphisms in a vector space. (Spanish: Una nueva clasificación de automorfismos en un espacio vectorial)
journal article
URL
https://docta.ucm.es/bitstreams/80921058-5c57-4fcb-b7d4-87d3c8bbc51c/download
File
MD5
0573a6162a721689f5d7cadbf57dfe4b
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application/pdf
Montesinos33.pdf
URL
https://docta.ucm.es/bitstreams/200ff0db-ca74-4ebe-807a-f36cb836688e/download
File
MD5
079c29eecdbc76266c6d1953626a925f
29289
text/plain
Montesinos33.pdf.txt