The common solution to matrix equations over a regular ring with applications

Indian Journal of Pure and Applied Mathematics

Volumn 36, Issue 12, 2005, Pages 655-672

  Wang, Qing Wen ^a   Qin, Feng ^a   Lin, Chun Yan ^b  

^a SHANGHAI UNIVERSITY   (China)

^b Shandong Finance Institute   (China)

Author keywords

Centrosymmetric Matrix; Inner Inverse of a Matrix; Reflexive Inverse of a Matrix; System Of Linear Matrix Equations; Von Neumann Regular Ring

Indexed keywords

EID: 33746097762     PISSN: 00195588     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. Morris P. L. Odell, Common solutions for q matrix equations with applications, J. Assn. Com. Mach., 15 (1968), 272-74.
2. P. Bhimasankaram, Common solutions to the linear matrix equations AX = B, CX = D, and EXF = G, Sankhya Ser. A, 38 (1976), 404-09.
3. 2, Proc. Cambridge Philos. Soc., 74 (1973), 213-16.
4. S. K. Mitra, A pair of simultaneous linear matrix equations and a matrix programming problem, Linear Algebra and Appl., 131 (1990), 97-123.
5. N. Shinozaki and M. Stbuya, Consistency of a pair of matrix equations with an application, Keio Engrg. Rep., 27 (1974), 141-46.
6. J. Van der Woulde, Feedback decoupling and stabilization for linear system with multiple exogenous variables, Ph.D. Thesis, Technical Univ. of Eindhoven, Netherlands, 1987.
7. J. Van der Woulde, Almost noninteracting control by measurement feedback, Systems Control Lett., 9 (1987), 7-16.
8. 2 with applications, Comput. Math. Appl., 41 (2001), 929-35.
9. Y. Tian, The solvability of two linear matrix equations, Linear and Multilinear Algebra, 48 (2000), 123-47.
10. A. B. Ozgiiler, N. Akar, A common solution to a pair of linear matrix equations over a principle domain, Linear Algebra Appl., 144 (1991), 85-99.
11. S. L. Blyumin, S. P. Milovidov, Investigation and solution of a pair of linear matrix equations. Mathematical Notes, 57(1-2) (1995), 211-13.
12. Q. W. Wang, J. H. Sun, 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), 169-82.
13. Q. W. Wang, A. Y. Wang, S. Z. Li, Bi(skew)symmetric and bipositive semidefinite solutions to a system of linear matrix equations over division rings, Math. Sci. Res. J., 6(7) (2002), 333-39.
14. 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.
15. Q. W. Wang, A System of Four Matrix Equations over von Neumann Regular Rings and Its Applications, Acta Math. Sinica, 21(2) (2005), 323-34.
16. C. Y. Lin, Q. W. Wang, New solvable conditions and a new expression of the general solution to a system of linear matrix equations over an arbitrary division ring, Southeast Asian Bulletin of Mathematics, 29(5) (2005), 755-62.
17. Q. W. Wang, The general solution to a system of real quaternion matrix equations, Comput. Math. Appl., 49 (2005), 665-75.
18. Q. W. Wang, Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations, Comput. Math. Appl., 49 (2005), 641-50.
19. A. C. Aitken, Determinants and Matrices, Oliver and Boyd, Edinburgh, 1939.
20. L. Datta and S. D. Morgera, On the reducibility of centrosymmetric matrices - applications in engineering problems, Circuits Systems Sig. Proc., 8(1) (1989), 71-96.
21. A. Cantoni and P. Butler, Eigenvalues and eigenvectors of symmetric centrosymmetric matrices. Linear Algebra Appl., 13 (1976), 275-88.
22. A. Lee, Centrohermitian and skew-centrohermitian matrices, Linear Algebra Appl., 29 (1980), 205-10.
23. R. D. Hell, R. G. Bates and S. R. Waters, On centrohermitian matrices, SIAM J. Matrix Anal. Appl., 11(1) (1990), 128-33.
24. A. L. Andrew, Centrosymmetric matrices, SIAM Rev., 40 (1998), 697-98.
25. I. S. Pressman, Matrices with multiple symmetry properties: applications of centrohermitian and perhermitian matrices, Linear Algebra Appl., 284 (1998), 239-58.
26. A. Melman, Symmetric centrosymmetric matrix-vector multiplication, Linear Algebra Appl., 320 (2000), 193-98.
27. S. L. Blyumin, S. P. Milovidov, Investigation and solution of matrix equations over associative rings. Comp. Math. Phys., 34(2) (1994), 133-42.
28. S. L. Blyumin, J. S. Golan, One-sided complements and solutions of the equation aXb = c in semirings, Int. J. of Math. and Math. Sciences, 29(8) (2002), 453-58.