P-(skew)symmetric common solutions to a pair of quaternion matrix equations

Applied Mathematics and Computation

Volumn 195, Issue 2, 2008, Pages 721-732

  Wang, Qing Wen ^a   Chang, Hai Xia ^a   Lin, Chun Yan ^b  

^a SHANGHAI UNIVERSITY   (China)

^b Shandong Finance Institute   (China)

Author keywords

Moore Penrose inverse; P skewsymmetric matrix; P symmetric matrix; Quaternion matrix; System of matrix equations

Indexed keywords

COMPUTATION THEORY; NONLINEAR EQUATIONS; NUMERICAL METHODS; PROBLEM SOLVING;

MATRIX EQUATIONS; MOORE-PENROSE INVERSES; P-SYMMETRIC MATRICES; QUATERNION MATRICES; SKEWSYMMETRIC SOLUTIONS;

MATRIX ALGEBRA;

EID: 37349037808     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.05.021     Document Type: Article

References (39)

1. Hungerford T.W. Algebra (1980), Spring-Verlag New York Inc.
2. Aitken A.C. Determinants and Matrices (1939), Oliver and Boyd, Edinburgh
3. Datta L., and Morgera S.D. On the reducibility of centrosymmetric matrices - applications in engineering problems. Circ. Syst. Sig. Process. 8 1 (1989) 71-96
4. Cantoni A., and Butler P. Eigenvalues and eigenvectors of symmetric centrosymmetric matrices. Linear Algebra Appl. 13 (1976) 275-288
5. Weaver J.R. Centrosymmetric (cross-symmetric) matrices, their basic properties, eigenvalues, eigenvectors. Amer. Math. Monthly 92 (1985) 711-717
6. Lee A. Centrohermitian and skew-centrohermitian matrices. Linear Algebra Appl. 29 (1980) 205-210
7. Hell R.D., Bates R.G., and Waters S.R. On centrohermitian matrices. SIAM J. Matrix Anal. Appl. 11 1 (1990) 128-133
8. Hell R.D., Bates R.G., and Waters S.R. On perhermitian matrices. SIAM J. Matrix Anal. Appl. 11 2 (1990) 173-179
9. Reid R.M. Some eigenvalues properties of persymmetric matrices. SIAM Rev. 39 (1997) 313-316
10. Andrew A.L. Centrosymmetric matrices. SIAM Rev. 40 (1998) 697-698
11. Pressman I.S. Matrices with multiple symmetry properties: applications of centrohermitian and perhermitian matrices. Linear Algebra Appl. 284 (1998) 239-258
12. Melman A. Symmetric centrosymmetric matrix-vector multiplication. Linear Algebra Appl. 320 (2000) 193-198
13. Wang Q.W., Sun J.H., and Li S.Z. Consistency for bi(skew)symmetric solutions to systems of generalized Sylvester equations over a finite central algebra. Linear Algebra Appl. 353 (2002) 169-182
14. Wang Q.W., Tian Y.G., and Li S.Z. Roth's theorems for centroselfconjugate solutions to systems of matrix equations over a finite dimensional central algebra. Southeast Asian Bull. Math. 27 (2004) 929-938
15. Wang Q.W. A system of four matrix equations over von Neumann regular rings and its applications. Acta Math. Sinica, English Series 21 2 (2005) 323-334
16. Wang Q.W., Qin F., and Lin C.Y. The common solution to matrix equations over a regular ring with applications. Indian J. Pure Appl. Math. 36 12 (2005) 655-672
17. Wang Q.W., and Li S.Z. The persymmetric and perskewsymmetric solutions to sets of matrix equations over a finite central algebra. Acta Math. Sinica 47 1 (2004) 27-34
18. Chen H.C., and Sameh A. Numerical linear algebra algorithms on the ceder system. In: Noor A.K. (Ed). Parallel Computations and Their Impact on Mechanics vol. 86 (1987), The American Society of Mechanical Engineering 101-125
19. Chen H.C. Generalized reflexive matrices: special properties and application. SIAM J. Matrix Anal. Appl. 19 (1998) 140-153
20. Trench W.F. Characterization and properties of matrices with generalized symmetry or skew symmetry. Linear Algebra Appl. 377 (2004) 207-218
21. Trench W.F. Inverse eigenproblems and associated approximation problems for matrices with generalized symmetry or skew symmetry. Linear Algebra Appl. 380 (2004) 199-211
22. Trench W.F. Hermitian, hermitian R-symmetric, and hermitian R-skew symmetric Procrustes problem. Linear Algebra Appl. 387 (2004) 83-98
23. Peng Z.Y., and Hu X.Y. The reflexive and anti-reflexive solutions of matrix equation AX = B. Linear Algebra Appl. 375 (2003) 147-155
24. HXB = C. J. Comput. Appl. Math. 200 2 (2007) 749-760
25. Cvetković-iliić D.S. The reflexive solutions of the matrix equation AXB = C. Comput. Math. Appl. 51 (2006) 897-902
26. Li F.L., Hu X.Y., and Zhang L. Left and right inverse eigenpairs problem of skew-centrosymmetric matrices. Appl. Math. Comput. 177 (2006) 105-110
27. Wang Q.W. Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations. Comput. Math. Appl. 49 5-6 (2005) 641-650
28. Wang Q.W. The general solution to a system of real quaternion matrix equations. Comput. Math. Appl. 49 5-6 (2005) 665-675
29. Wang Q.W. A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity. Linear Algebra Appl. 384 (2004) 43-54
30. Baksalary J.K., and Kala R. The matrix equation AXB + CYD = E. Linear Algebra Appl. 30 (1980) 141-147
31. Özgüler A.B. The matrix equation AXB + CYD = E over a principal ideal domain. SIAM J. Matrix Anal. Appl. 12 (1991) 581-591
32. Huang L., and Zeng Q. The solvability of matrix equation AXB + CYD = E over a simple Artinian ring. Linear and Multilinear Algebra 38 (1995) 225-232
33. Huang L. The solvability of matrix equation AXB + CYD = E over a ring. Adv. Math. (China) 26 3 (1997) 269-275 (in Chinese)
34. Blyumin S.L., and Milovidov S.P. Investigation and solution of matrix equations over associative rings. Comput. Math. Phys. 34 2 (1994) 133-142
35. Blyumin S.L., and S Golan J. One-sided complements and solutions of the equation aXb = c in semirings. Int. J. Math. Math. Sci. 29 8 (2002) 453-458
36. Tian Y. Ranks of Solutions of the matrix equation AXB = C. Linear and Multilinear Algebra 51 2 (2003) 111-125
37. Wang Q.W., Wu Z.C., and Lin C.Y. Extremal ranks of a quaternion matrix expression subject to consistent systems of quaternion matrix equations with applications. Appl. Math. Comput. 182 (2006) 1755-1764
38. Wang Q.W., Song G.J., and Lin C.Y. Extreme ranks of the solution to a consistent system of linear quaternion matrix equations with an application. Appl. Math. Comput. (2007) 10.1016/j.amc.2006.12.039
39. Q.W. Wang, S.W. Yu, C.Y. Lin, Extreme ranks of a linear quaternion matrix expression subject to triple quaternion matrix equations with applications, Appl. Math. Comput. (2007), doi:10.1016/j.amc.2007.05.018.