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Tytuł artykułu

Companion matrices and their relations to Toeplitz and Hankel matrices

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper we describe some properties of companion matrices and demonstrate some special patterns that arisewhen a Toeplitz or a Hankel matrix is multiplied by a related companion matrix.We present a necessary and sufficient condition, generalizing known results, for a matrix to be the transforming matrix for a similarity between a pair of companion matrices. A special case of our main result shows that a Toeplitz or a Hankel matrix can be extended using associated companion matrices, preserving the Toeplitz or Hankel structure respectively.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
3
Numer
1
Opis fizyczny
Daty
otrzymano
2015-04-22
zaakceptowano
2015-09-15
online
2015-10-07
Twórcy
autor
  • Luo: School of Mathematical and Geospatial Sciences, RMIT University, GPO Box 2476V,
    Melbourne, Vic. 3001, AUSTRALIA
autor
  • Department of Electrical and Electronic Engineering, University of Melbourne, Vic. 3010, AUSTRALIA
Bibliografia
  • [1] Yu. A. Al’pin and S. N. Il’in, Infinite extensions of Toeplitz matrices, J. Math. Sci. (N. Y.), Vol. 127, No. 3, 1957 - 1961, (2005).
  • [2] D. Bini, V. Pan, Eflcient algorithms for the evaluation of the eigenvalues of (block) banded Toeplitz matrices, Math. Comp.50, 431-448, (1988).
  • [3] Louis Brand, Companion matrix and its properties, Amer. Math. Monthly, Vol. 71, No. 6, 629 - 634, (1964).
  • [4] Z. Cinkir, A fast elementary algorithm for computing the determinant of Toeplitz matrices, J. Comput. Appl. Math, Vol. 255,353-361, (2014).
  • [5] I. Gohberg and A. Semencul, On the inversion of finite Toeplitz matrices and their continuous analogs, Mat. Issled. 7 (2),201-223 (1972).
  • [6] Georg Heinig and Karla Rost, Introduction to Bezoutians, Operator Theory: Advances and Applications, Vol. 199, 25 - 118,(2010).
  • [7] Georg Heinig and Karla Rost, Algebraic methods for Toeplitz-like matrices and operators, Operator Theory: Advances andApplications, Vol. 13, Birkhäuser Verlag, Basel, (1984).
  • [8] R. Hill, Y. Luo and U. Schwerdtfeger, Exact solutions to a two-block l1 optimal control problem, Porceedings of the 7th IFACSymposium on Robust Control Design, ROCOND’12, Jakob Stoustrup, Elsevier, United Kingdom, pp. 461-466 ( 2012)
  • [9] Thomas Kailath, Linear System, Prentice-Hall, Inc., (1980).
  • [10] F. I. Lander, The Bezoutian and the inversion of Hankel and Toeplitz matrices (in Russian),Mat. Issled., Vol. 9, 69–87, (1974).
  • [11] Arthur Lim and Jialing Dai On product of companion matrices, Linear Algebra Appl., Vol. 435, Issue 11, 2921–2935, (2011).[WoS]
  • [12] David G. Luenberger, Introduction to Dynamic Systems: Theory,Models, and Applications, JohnWiley&Sons, Inc., New York,(1979).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_spma-2015-0021
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