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The centralizer of an endomorphism over an arbitrary field

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The centralizer of an endomorphism over an arbitrary field

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Mingueza, D.; Montoro, ME.; Roca Martinez, A. (2020). The centralizer of an endomorphism over an arbitrary field. Linear Algebra and its Applications. 591:322-351. https://doi.org/10.1016/j.laa.2020.01.013

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Título: The centralizer of an endomorphism over an arbitrary field
Autor: Mingueza, David Montoro, M. Eulàlia Roca Martinez, Alicia
Entidad UPV: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Fecha difusión:
Resumen:
[EN] The centralizer of an endomorphism of a finite dimensional vector space is known when the endomorphism is nonderogatory or when its minimal polynomial splits over the field. It is also known for the real Jordan canonical ...[+]
Palabras clave: Centralizer , Companion matrices , Nonseparable polynomials , Generalized Jordan canonical form , Generalized Weyr canonical form
Derechos de uso: Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
Fuente:
Linear Algebra and its Applications. (issn: 0024-3795 )
DOI: 10.1016/j.laa.2020.01.013
Editorial:
Elsevier
Versión del editor: https://doi.org/10.1016/j.laa.2020.01.013
Código del Proyecto:
info:eu-repo/grantAgreement/AEI//MTM2017-90682-REDT/ES/RED TEMATICA DE ALGEBRA LINEAL, ANALISIS MATRICIAL Y APLICACIONES/
info:eu-repo/grantAgreement/MINECO//MTM2015-65361-P/ES/VARIEDADES ALGEBRAICAS, LINEALES Y DIFERENCIABLES, ARITMETICA Y MODULI/
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-83624-P/ES/MODELOS POLINOMIALES, SISTEMAS CUADRATICOS Y MATRICES: ESTRUCTURA, LINEALIZACIONES Y PERTURBACION/
Agradecimientos:
The second author is partially supported by "Ministerio de Economía, Industria y Competitividad (MINECO)" of Spain and "Fondo Europeo de Desarrollo Regional (FEDER)" of EU through grants MTM2015-65361-P and MTM2017-90682-REDT. ...[+]
Tipo: Artículo

References

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Asaeda, Y. (1993). A remark to the paper «On the stabilizer of companion matrices» by J. Gomez-Calderon. Proceedings of the Japan Academy, Series A, Mathematical Sciences, 69(6). doi:10.3792/pjaa.69.170

Brickman, L., & Fillmore, P. A. (1967). The Invariant Subspace Lattice of a Linear Transformation. Canadian Journal of Mathematics, 19, 810-822. doi:10.4153/cjm-1967-075-4 [+]
Astuti, P., & Wimmer, H. K. (2009). Hyperinvariant, characteristic and marked subspaces. Operators and Matrices, (2), 261-270. doi:10.7153/oam-03-16

Asaeda, Y. (1993). A remark to the paper «On the stabilizer of companion matrices» by J. Gomez-Calderon. Proceedings of the Japan Academy, Series A, Mathematical Sciences, 69(6). doi:10.3792/pjaa.69.170

Brickman, L., & Fillmore, P. A. (1967). The Invariant Subspace Lattice of a Linear Transformation. Canadian Journal of Mathematics, 19, 810-822. doi:10.4153/cjm-1967-075-4

Dalalyan, S. H. (2014). Generalized Jordan Normal Forms of Linear Operators. Journal of Mathematical Sciences, 198(5), 498-504. doi:10.1007/s10958-014-1805-3

Ferrer, J., Mingueza, D., & Montoro, M. E. (2013). Determinant of a matrix that commutes with a Jordan matrix. Linear Algebra and its Applications, 439(12), 3945-3954. doi:10.1016/j.laa.2013.10.023

Gomez-Calderon, J. (1993). On the stabilizer of companion matrices. Proceedings of the Japan Academy, Series A, Mathematical Sciences, 69(5). doi:10.3792/pjaa.69.140

Fillmore, P. A., Herrero, D. A., & Longstaff, W. E. (1977). The hyperinvariant subspace lattice of a linear transformation. Linear Algebra and its Applications, 17(2), 125-132. doi:10.1016/0024-3795(77)90032-5

Holtz, O. (2000). Applications of the duality method to generalizations of the Jordan canonical form. Linear Algebra and its Applications, 310(1-3), 11-17. doi:10.1016/s0024-3795(00)00054-9

Mingueza, D., Eulàlia Montoro, M., & Pacha, J. R. (2013). Description of characteristic non-hyperinvariant subspaces over the fieldGF(2). Linear Algebra and its Applications, 439(12), 3734-3745. doi:10.1016/j.laa.2013.10.025

Mingueza, D., Montoro, M. E., & Roca, A. (2018). The lattice of characteristic subspaces of an endomorphism with Jordan–Chevalley decomposition. Linear Algebra and its Applications, 558, 63-73. doi:10.1016/j.laa.2018.08.005

Robinson, D. W. (1965). On Matrix Commutators of Higher Order. Canadian Journal of Mathematics, 17, 527-532. doi:10.4153/cjm-1965-052-9

Robinson, D. W. (1970). The Generalized Jordan Canonical Form. The American Mathematical Monthly, 77(4), 392-395. doi:10.1080/00029890.1970.11992500

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