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

Xian Zhang

Journal of Multivariate Analysis, 2005, vol. 93, issue 2, 257-266

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).

Keywords: Hermitian; (symmetric); nonnegative-definite; solution; Hermitian; (symmetric); positive-definite; solution; Matrix; equation; Kernel; space; Column; space; Moore-Penrose; generalized; inverse; Linear; hypothesis; Multivariate; linear; model (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (1)

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