Skip to main content
SpringerLink
Log in

Generalized bipositive semidefinite solutions to a system of matrix equations

  • Published:
Journal of Shanghai University (English Edition)

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Trench W F. Hermitian, Hermitian R-symmetric, and Hermitian R-skew symmetric Procruste problems[J]. Linear Algebra and Its Applications, 2004, 387: 83–98.

    Article  MATH  MathSciNet  Google Scholar 

  2. Trench W F. Characterization and properties of matrices with generalized symmetry or skew symmetry[J]. Linear Algebra and Its Applications, 2004, 377: 207–218.

    Article  MATH  MathSciNet  Google Scholar 

  3. 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.

    MATH  MathSciNet  Google Scholar 

  4. Chu K E. Symmetric solutions of linear matrix equations by matrix decomposition[J]. Linear Algebra and Its Applications, 1989, 119: 35–50.

    Article  MATH  MathSciNet  Google Scholar 

  5. Dai H. On the symmetric solution of linear matrix equations[J]. Linear Algebra and Its Applications, 1990, 131: 1–7.

    Article  MATH  MathSciNet  Google Scholar 

  6. Henk Don F J. On the symmetric solutions of a linear matrix equation[J]. Linear Algebra and Its Applications, 1987, 93: 1–7.

    Article  MATH  MathSciNet  Google Scholar 

  7. Vetter W J. Vector structures and solutions of linear matrix equations[J]. Linear Algebra and Its Applications, 1975, 10: 181–188.

    Article  MATH  MathSciNet  Google Scholar 

  8. 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.

    Article  MATH  MathSciNet  Google Scholar 

  9. Wu L. The re-positive definite solutions to the matrix inverse problem AX = B[J]. Linear Algebra and Its Applications, 1992, 174: 145–151.

    MATH  MathSciNet  Google Scholar 

  10. 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.

    MATH  MathSciNet  Google Scholar 

  11. 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.

    Article  MATH  MathSciNet  Google Scholar 

  12. 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.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, College of Sciences, Shanghai University, Shanghai, 200444, P. R. China

    Yu Shao-wen  (俞绍文) & Wang Qing-wen PhD  (王卿文) (Prof.)

  2. School of Statistics and Sciences, University of Finance of Shandong, Jinan, 250014, P. R. China

    Lin Chun-yan  (林春艳)

Authors
  1. Yu Shao-wen  (俞绍文)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wang Qing-wen PhD  (王卿文)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lin Chun-yan  (林春艳)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wang Qing-wen PhD  (王卿文).

Additional information

Project supported by the National Natural Science Foundation of China (Grant No.60672160)

About this article

Cite this article

Yu, Sw., Wang, Qw. & Lin, Cy. Generalized bipositive semidefinite solutions to a system of matrix equations. J. of Shanghai Univ. 11, 106–108 (2007). https://doi.org/10.1007/s11741-007-0203-1

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11741-007-0203-1

Keywords

2000 Mathematics Subject Classification

Search

Navigation