Bilinear characterizations of companion matrices

Minghua Lin; Harald K. Wimmer

Special Matrices (2014)

  • Volume: 2, Issue: 1, page 99-105, electronic only
  • ISSN: 2300-7451

Abstract

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Companion matrices of the second type are characterized by properties that involve bilinear maps.

How to cite

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Minghua Lin, and Harald K. Wimmer. "Bilinear characterizations of companion matrices." Special Matrices 2.1 (2014): 99-105, electronic only. <http://eudml.org/doc/267175>.

@article{MinghuaLin2014,
abstract = {Companion matrices of the second type are characterized by properties that involve bilinear maps.},
author = {Minghua Lin, Harald K. Wimmer},
journal = {Special Matrices},
keywords = {Companion matrix; reachability matrix; bilinear map; companion matrix},
language = {eng},
number = {1},
pages = {99-105, electronic only},
title = {Bilinear characterizations of companion matrices},
url = {http://eudml.org/doc/267175},
volume = {2},
year = {2014},
}

TY - JOUR
AU - Minghua Lin
AU - Harald K. Wimmer
TI - Bilinear characterizations of companion matrices
JO - Special Matrices
PY - 2014
VL - 2
IS - 1
SP - 99
EP - 105, electronic only
AB - Companion matrices of the second type are characterized by properties that involve bilinear maps.
LA - eng
KW - Companion matrix; reachability matrix; bilinear map; companion matrix
UR - http://eudml.org/doc/267175
ER -

References

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  1. [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. [2] A. J. Brzezinski, Output-Only Techniques for Fault Detection, Dissertation, Department of Aerospace Engineering, University of Michigan, Ann Arbor, 2011. 
  3. [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. [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. [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] Zbl1281.15004
  6. [6] A. Ferrante and H. K. Wimmer, Reachability matrices and cyclic matrices, Electron. J. Linear Algebra 20, 95–102 (2010). Zbl1198.15009
  7. [7] I. Gohberg, P. Lancaster, and L. Rodman, Matrix Polynomials, Academic Press, New York, 1982. Zbl0482.15001
  8. [8] M. L. J. Hautus, Operator substitution, Linear Algebra Appl. 205–206, 713–739 (1994). Zbl0806.47012
  9. [9] Th. Kailath, Linear Systems, Prentice Hall, Englewood Cliffs, 1980. 

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