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

Guangjing Song and Shaowen Yu

Applied Mathematics and Computation, 2018, vol. 338, issue C, 828-841

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.

Keywords: Matrix equation; Nonnegative definite solution; Positive definite solution; Rank; Inertia (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:338:y:2018:i:c:p:828-841

DOI: 10.1016/j.amc.2018.06.045

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