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The general common Hermitian nonnegative-definite solution to the matrix equations AXA*=BB* and CXC*=DD* with applications in statistics

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  • Zhang, Xian

Abstract

We deduce a necessary and sufficient condition for the matrix equations AXA*=BB* and CXC*=DD* to have a common Hermitian nonnegative-definite solution and a representation of the general common Hermitian nonnegative-definite solution to these two equations when they have such common solutions. Thereby, we solve a statistical problem which is concerned in testing linear hypotheses about regression coefficients in the multivariate linear model. This paper is a revision of Young et al. (J. Multivariate Anal. 68 (1999) 165) whose mistake was pointed out in (Linear Algebra Appl. 321 (2000) 123).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:93:y:2005:i:2:p:257-266
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Liu, Xifu, 2015. "The Hermitian solution of AXA*=B subject to CXC* ≥ D," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 890-898.

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