The (R,S)-symmetric and (R,S)-skew symmetric solutions of the pair of matrix equations A 1XB 1 = C 1 and A 2XB 2 = C 2

Bulletin of the Iranian Mathematical Society

Volumn 37, Issue 3, 2011, Pages 269-279

  Dehghan, M ^a   Hajarian, M ^b  

^a AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

^b SHAHID BEHESHTI UNIVERSITY   (Iran)

Author keywords

(R S) skew symmetric matrix; (R S) symmetric matrix; Matrix equation

Indexed keywords

EID: 84858613324     PISSN: 10186301     EISSN: 1017060X     Source Type: Journal    
DOI: None     Document Type: Article

References (31)

1. H. C. Chen, Generalized reflexive matrices: special properties and applications, SIAM J. Matrix Anal. Appl. 19 (1998) 140-153.
2. K. E. Chu, Symmetric solutions of linear matrix equations by matrix decompositions, Linear Algebra Appl. 119 (1989) 35-50.
3. H. Dai, On the symmetric solutions of linear matrix equations, Linear Algebra Appl. 131 (1990) 1-7.
4. M. Dehghan and M. Hajarian, An iterative algorithm for the reflexive solutions of the generalized coupled Sylvester matrix equations and its optimal approximation, Appl. Math. Comput. 202 (2008) 571-588.
5. M. Dehghan and M. Hajarian, Finite iterative algorithms for the reflexive and anti-reflexive solutions of the matrix equation A1X1B1 + A2X2B2 = C, Math. Comput. Modelling 49 (2009) 1937-1959.
6. 2-AV F -CV = BW, IET Control Theory Appl. 3 (2009) 1401-1408.
7. M. Dehghan and M. Hajarian, The general coupled matrix equations over generalized bisymmetric matrices, Linear Algebra Appl. 432 (2010) 1531-1552.
8. M. Dehghan and M. Hajarian, An efficient algorithm for solving general coupled matrix equations and its application, Math. Comput. Modeling 51 (2010) 1118-1134.
9. M. Dehghan and M. Hajarian, The reflexive and anti-reflexive solutions of a linear matrix equation and systems of matrix equations, Rocky Mountain J. Math. 40(3) (2010) 825-848.
10. F. Ding and T. Chen and Gradient based iterative algorithms for solving a class of matrix equations, IEEE Trans. Automat. Control 50 (2005) 1216-1221.
11. F. Ding and P. X. Liu and J. Ding, Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle, Appl. Math. Comput. 197 (2008) 41-50.
12. F. Ding and T. Chen, Hierarchical gradient-based identification of multivariable discrete-time systems. Automatica J. IFAC 41 (2005) 315-325.
13. F. Ding, T. Chen, Iterative least squares solutions of coupled Sylvester matrix equations. Systems Control Lett. 54 (2005) 95-107.
14. F. Ding and T. Chen, On iterative solutions of general coupled matrix equations, SIAM J. Control Optim. 44 (2006) 2269-2284.
15. F. Ding and T. Chen, Hierarchical least squares identification methods for multivariable systems, IEEE Trans. Automat. Control 50 (2005) 397-402.
16. A. Liao and D. X. Xie, Least-squares solution of a class of inverse eigenvalue problems for bisymmetric nonnegative definite matrices, (Chinese), Math. Numer. Sin. 23(2) (2001) 209-218.
17. S. K. Mitra and Common solutions to a pair of linear matrix equations A1XB1 = C1 and A2XB2 = C2, Proc. Cambridge Philos. Soc. 74 (1973) 213-216.
18. S. K. Mitra and A pair of simultaneous linear matrix equations A1XB1 = C1, A2XB2 = C2 and a matrix programming problem, Linear Algebra Appl. 131 (1990) 107-123.
19. A. Navarra, P. L. Odell and D.M. Young, A representation of the general common solution to the matrix equations A1XB1 = C1 and A2XB2 = C2 with applications, Comput. Math. Appl. 41 (2001) 929-935.
20. -2A = I, Int. J. Comput. Math. 82 (2005) 865-870.
21. M. A. Ramadan and E. A. El-Sayed, On the matrix equation XH = HX and the associated controllability problem, Appl. Math. Comput. 186 (2007) 844-859.
22. W. F. Trench, Minimization problems for (R, S)-symmetric and (R, S)-skew symmetric matrices, Linear Algebra Appl. 389 (2004) 23-31.
23. Q. W. Wang, J. H. Sun and S. Z. Li, Consistency for bi(skew)symmetric solutions to systems of generalized Sylvester equations over a finite central algebra, Linear Algebra Appl. 353 (2002) 169-182.
24. Q. W. Wang, A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity, Linear Algebra Appl. 384 (2004) 43-54.
25. Q. W. Wang, Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations, Comput. Math. Appl. 49 (2005) 641-650.
26. Q. W. Wang and F. Zhang, The reflexive re-nonnegative definite solution to a quaternion matrix equation, Electron. J. Linear Algebra 17 (2008) 88-101.
27. K. G. Woodgate, Least-squares solution of F = PG over positive semidefinite symmetric P, Linear Algebra Appl. 245 (1996) 171-190.
28. D. X. Xie and L. Zhang, Least squares solutions of inverse problems for a class of anti-symmetric matrices, (Chinese), Gongcheng Shuxue Xuebao 10(4) (1993) 25-34.
29. B. Zhou and G. R. Duan, A new solution to the generalized Sylvester matrix equation AV - EV F = BW, Systems Control Lett. 55 (2006) 193-198.
30. B. Zhou and G. R. Duan, On the generalized Sylvester mapping and matrix equations, Systems Control Lett. 57 (2008) 200-208.
31. B. Zhou, Z. Y. Li, G. R. Duan and Y. Wang, Weighted least squares solutions to general coupled Sylvester matrix equations, J. Comput. Appl. Math. 224 (2009) 759-776.