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On the existence of a common eigenvector for all matrices in the commutant of a single matrix

Author
Magret, M. D.; Montoro, M.
Type of activity
Journal article
Journal
Linear algebra and its applications
Date of publication
2012-09
Volume
437
Number
5
First page
1285
Last page
1292
DOI
https://doi.org/10.1016/j.laa.2012.04.011 Open in new window
Repository
http://hdl.handle.net/2117/17364 Open in new window
URL
http://www.sciencedirect.com/science/journal/00243795/437/5 Open in new window
Abstract
The main purpose of this paper is to study common invariant subspaces of any matrix in the centralizer of a given matrix A∈Mn(F), where F denotes an algebraically closed field. In particular, we obtain a necessary and sufficient condition for the existence of a common eigenvector for all the matrices in this set.
Citation
Magret, M. D.; Montoro, M. On the existence of a common eigenvector for all matrices in the commutant of a single matrix. "Linear algebra and its applications", Setembre 2012, vol. 437, núm. 5, p. 1285-1292.
Group of research
EGSA - Differential Equations, Geometry, Control and Dynamical Systems, and Applications
SCL-EG - Linear Control Systems: a Geometric Approach