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Determinant of a matrix that commutes with a Jordan matrix

Author
Montoro, M.; Ferrer, J.; Mingueza, D.
Type of activity
Journal article
Journal
Linear algebra and its applications
Date of publication
2013-10-30
Volume
439
Number
12
First page
3945
Last page
3954
DOI
https://doi.org/10.1016/j.laa.2013.10.023 Open in new window
Repository
http://hdl.handle.net/2117/21026 Open in new window
URL
http://authors.elsevier.com/sd/article/S0024379513006447 Open in new window
Abstract
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 ...
Citation
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.
Group of research
EGSA - Differential Equations, Geometry, Control and Dynamical Systems, and Applications
SCL-EG - Linear Control Systems: a Geometric Approach

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