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

Authors:
Xian Zhang
Affiliations:
Department of Mathematics, Heilongjiang University, Harbin 150080, PR China and School of Mechanical and Manufacturing Engineering, The Queen's University of Belfast, Ashby Bldg., Stranmillis Road ...
Venue:
Journal of Multivariate Analysis
Year:
2005

Citing 1
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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).