JOURNAL BROWSE
Search
Advanced SearchSearch Tips
THE SOLUTIONS OF SOME OPERATOR EQUATIONS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
THE SOLUTIONS OF SOME OPERATOR EQUATIONS
Cvetkovic-Ilic, Dragana S.;
  PDF(new window)
 Abstract
In this paper we consider the solvability and describe the set of the solutions of the operator equations and . This generalizes the results of D. S. Djordjevic [Explicit solution of the operator equation A=B
 Keywords
operator equation;Moore-Penrose inverse;g-invertibility;
 Language
English
 Cited by
1.
ON THE REFLEXIVE SOLUTIONS OF THE MATRIX EQUATION AXB + CYD = E,;;

대한수학회보, 2009. vol.46. 3, pp.511-519 crossref(new window)
1.
Maximization and minimization of the rank and inertia of the Hermitian matrix expression A-BX-(BX)* with applications, Linear Algebra and its Applications, 2011, 434, 10, 2109  crossref(new windwow)
 References
1.
A. Ben-Israel and T. N. E. Greville, Generalized Inverses, Theory and applications. Second edition. CMS Books in Mathematics/Ouvrages de Mathematiques de la SMC, 15. Springer-Verlag, New York, 2003

2.
S. L. Campbell and C. D. Meyer Jr., Generalized Inverses of Linear Transformations, Corrected reprint of the 1979 original. Dover Publications, Inc., New York, 1991

3.
S. R. Caradus, Generalized Inverses and Operator Theory, Queen's Papers in Pure and Applied Mathematics, 50. Queen's University, Kingston, Ont., 1978

4.
D. S. Djordjevic, Explicit solution of the operator equation $A^{*}$X+$X^{*}$A = B, J. Comput. Appl. Math. 200 (2007), no. 2, 701-704 crossref(new window)

5.
R. E. Harte, Invertibility and singularity for bounded linear operators, Monographs and Textbooks in Pure and Applied Mathematics, 109. Marcel Dekker, Inc., New York, 1988

6.
P. Kirrinnis, Fast algorithms for the Sylvester equation AX - X$B^{T}$= C, Theoret. Comput. Sci. 259 (2001), no. 1-2, 623-638 crossref(new window)

7.
G. Kitagawa, An algorithm for solving the matrix equation X = FX$F^{T}$ + S , International Journal of Control, 25 (1977), no. 5, 745-753 crossref(new window)

8.
Y. X. Peng, X. Y. Hu, and L. Zhang, An iteration method for the symmetric solutions and the optimal approximation solution of the matrix equation AXB = C, Appl. Math. Comput. 160 (2005), no. 3, 763-777 crossref(new window)

9.
Z. Y. Peng and X. Y. Hu, The reflexive and anti-reflexive solutions of the matrix equation AX = B, Linear Algebra Appl. 375 (2003), 147-155 crossref(new window)

10.
D. C. Sorensen and A. C. Antoulas, The Sylvester equation and approximate balanced reduction, Linear Algebra Appl. 351/352 (2002), 671-700