Companion matrices of the second type are characterized by properties that involve bilinear maps.
@article{bwmeta1.element.doi-10_2478_spma-2014-0010, author = {Minghua Lin and Harald K. Wimmer}, title = {Bilinear characterizations of companion matrices}, journal = {Special Matrices}, volume = {2}, year = {2014}, zbl = {1291.15004}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_spma-2014-0010} }
Minghua Lin; Harald K. Wimmer. Bilinear characterizations of companion matrices. Special Matrices, Tome 2 (2014) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_spma-2014-0010/
[1] H. Bart and G. Ph. A. Thijsse, Simultaneous reduction to companion and triangular forms of sets of matrices, Linear Multilinear Algebra 26, 231–241 (1990). [Crossref]
[2] A. J. Brzezinski, Output-Only Techniques for Fault Detection, Dissertation, Department of Aerospace Engineering, University of Michigan, Ann Arbor, 2011.
[3] A. J. Brzezinski, E. Wu, and D. S. Bernstein, Curiously commuting vectors, Problem 44-3, IMAGE (Bulletin of the International Linear Algebra Society) 44 (2010).
[4] A. J. Brzezinski, S. Kukreja, Jun Ni, and D. S. Bernstein, Sensor-only fault detection using pseudo transfer function identification, in Proc. Amer. Contr. Conf., 5433–5438, Baltimore, June 2010.
[5] F. De Terán, F. M. Dopico, and J. Pérez, Condition numbers for inversion of Fiedler matrices, Linear Algebra Appl. 439, 944–981 (2013). [WoS] | Zbl 1281.15004
[6] A. Ferrante and H. K. Wimmer, Reachability matrices and cyclic matrices, Electron. J. Linear Algebra 20, 95–102 (2010). | Zbl 1198.15009
[7] I. Gohberg, P. Lancaster, and L. Rodman, Matrix Polynomials, Academic Press, New York, 1982. | Zbl 0482.15001
[8] M. L. J. Hautus, Operator substitution, Linear Algebra Appl. 205–206, 713–739 (1994). | Zbl 0806.47012
[9] Th. Kailath, Linear Systems, Prentice Hall, Englewood Cliffs, 1980.