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Determinant of a matrix that commutes with a Jordan matrix

Autor
Montoro, M.; Ferrer, J.; Mingueza, D.
Tipus d'activitat
Article en revista
Revista
Linear algebra and its applications
Data de publicació
2013-10-30
Volum
439
Número
12
Pàgina inicial
3945
Pàgina final
3954
DOI
https://doi.org/10.1016/j.laa.2013.10.023 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/21026 Obrir en finestra nova
URL
http://authors.elsevier.com/sd/article/S0024379513006447 Obrir en finestra nova
Resum
Let F be an arbitrary field, Mn(F) the set of all matrices n×n over F and J¿Mn(F) a Jordan matrix. In this paper, we obtain an explicit formula for the determinant of any matrix that commutes with J, i.e., the determinant of any element T¿Z(J), the centralizer of J. Our result can also be extended to any T'¿Z(A), where A¿Mn(F), can be reduced to J=S-1AS. This is because T=S-1T'S¿Z(J), and clearly View the MathML source. If F is algebraically closed, any matrix A can be reduced in this way ...
Citació
Montoro, M.; Ferrer, J.; Mingueza, D. Determinant of a matrix that commutes with a Jordan matrix. "Linear algebra and its applications", 30 Octubre 2013, vol. 439, núm. 12, p. 3945-3954.
Grup de recerca
EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
SCL-EG - Sistemes de Control Lineals: estudi Geomètric

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