IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v338y2018icp828-841.html
   My bibliography  Save this article

Nonnegative definite and Re-nonnegative definite solutions to a system of matrix equations with statistical applications

Author

Listed:
  • Song, Guangjing
  • Yu, Shaowen

Abstract

Necessary and sufficient conditions are given for the existence of a nonnegative definite solution, a Re-nonnegative definite solution, a positive definite solution and a Re-positive definite solution to the system of matrix equations AXA*=CandBXB*=D,respectively. The expressions for these special solutions are given when the consistent conditions are satisfied. Based on the new results, the characterization of the covariance matrix such that a pair of multivariate quadratic forms are distributed as independent noncentral Wishart random matrices is derived. Many results existing in the literature are extended.

Suggested Citation

  • Song, Guangjing & Yu, Shaowen, 2018. "Nonnegative definite and Re-nonnegative definite solutions to a system of matrix equations with statistical applications," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 828-841.
    • Handle: RePEc:eee:apmaco:v:338:y:2018:i:c:p:828-841
    DOI: 10.1016/j.amc.2018.06.045
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318305344
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.06.045?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Tongsong Jiang & Xuehan Cheng & Sitao Ling, 2014. "An Algebraic Relation between Consimilarity and Similarity of Quaternion Matrices and Applications," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-5, September.
    2. Young, Dean M. & Seaman, John W. & Meaux, Laurie M., 1999. "Independence Distribution Preserving Covariance Structures for the Multivariate Linear Model," Journal of Multivariate Analysis, Elsevier, vol. 68(2), pages 165-175, February.
    3. Yonghui Liu & Yongge Tian, 2011. "Max-Min Problems on the Ranks and Inertias of the Matrix Expressions A−BXC±(BXC)∗ with Applications," Journal of Optimization Theory and Applications, Springer, vol. 148(3), pages 593-622, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Phil D. Young & Dean M. Young, 2016. "Characterizations of Noncentral Chi-Squared-Generating Covariance Structures for a Normally Distributed Random Vector," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(2), pages 231-247, August.
    2. Jiang, Bo & Tian, Yongge, 2017. "Rank/inertia approaches to weighted least-squares solutions of linear matrix equations," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 400-413.
    3. Yongge Tian & Bo Jiang, 2017. "Quadratic properties of least-squares solutions of linear matrix equations with statistical applications," Computational Statistics, Springer, vol. 32(4), pages 1645-1663, December.
    4. Shanshan Hu & Yongxin Yuan, 2023. "Common Solutions to the Matrix Equations $$AX=B$$ A X = B and $$XC=D$$ X C = D on a Subspace," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 372-386, July.
    5. Shao-Wen Yu, 2012. "The Real and Complex Hermitian Solutions to a System of Quaternion Matrix Equations with Applications," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-19, January.
    6. Zhang, Xian, 2005. "The general common Hermitian nonnegative-definite solution to the matrix equations AXA*=BB* and CXC*=DD* with applications in statistics," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 257-266, April.
    7. Liu, Xifu, 2015. "The Hermitian solution of AXA*=B subject to CXC* ≥ D," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 890-898.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:338:y:2018:i:c:p:828-841. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.