Generalized bipositive semidefinite solutions to a system of matrix equations

Journal of Shanghai University (English Edition) - Tập 11 - Trang 106-108 - 2007
Shao-wen Yu, Qing-wen Wang1, Chun-yan Lin2
1Department of Mathematics, College of Sciences, Shanghai University, Shanghai, P. R. China
2School of Statistics and Sciences, University of Finance of Shandong, Jinan, P. R. China

Tóm tắt

In this paper, a system of complex matrix equations was studied. Necessary and sufficient conditions for the existence and the expression of generalized bipositive semidefinite solution to the system were given. In addition, a criterion for a matrix to be generalized bipositive semidefinite was determined.

Tài liệu tham khảo

Trench W F. Hermitian, Hermitian R-symmetric, and Hermitian R-skew symmetric Procruste problems[J]. Linear Algebra and Its Applications, 2004, 387: 83–98. Trench W F. Characterization and properties of matrices with generalized symmetry or skew symmetry[J]. Linear Algebra and Its Applications, 2004, 377: 207–218. Wang Q W, Yang C L. The re-nonnegative definite solutions to the matrix equation AXB = C[J]. Commentationes Mathematicae Universitatis Carolinae, 1998, 39: 7–13. Chu K E. Symmetric solutions of linear matrix equations by matrix decomposition[J]. Linear Algebra and Its Applications, 1989, 119: 35–50. Dai H. On the symmetric solution of linear matrix equations[J]. Linear Algebra and Its Applications, 1990, 131: 1–7. Henk Don F J. On the symmetric solutions of a linear matrix equation[J]. Linear Algebra and Its Applications, 1987, 93: 1–7. Vetter W J. Vector structures and solutions of linear matrix equations[J]. Linear Algebra and Its Applications, 1975, 10: 181–188. Khatri C G, Mitra S K. Hermitian and nonnegative definite solutions of linear matrix equations[J]. SIAM Journal on Applied Mathematics, 1976, 31: 579–585. Wu L. The re-positive definite solutions to the matrix inverse problem AX = B[J]. Linear Algebra and Its Applications, 1992, 174: 145–151. Wang Q W, Li S Z. On the center(skew-)selfconjugate solutions to the systems of matrix equations over a finite dimensional central algebra[J]. Mathematical Sciences Research Hot-Line, 2001, 5(12): 11–17. Wang Q W, Sun J H, Li S Z. Consistency for bi(skew)symmetric solutions to systems of generalized Sylvester equations over a finite central algebra[J]. Linear Algebra and Its Applications, 2002, 353: 169–182. Peng Z Y, Hu X Y. The reflexive and anti-reflexive solutions of the matrix equation AX = B[J]. Linear Algebra and Its Applications, 2003, 375: 147–155.