文献类型：期刊文献

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

作者：Song, Guangjing[1];Yu, Shaowen[2]

机构：[1]Weifang Univ, Sch Math & Informat Sci, Weifang 261061, Peoples R China;[2]East China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2018

卷号：338

起止页码：828

外文期刊名：APPLIED MATHEMATICS AND COMPUTATION

收录：;EI(收录号：20183105643119);WOS:【SCI-EXPANDED(收录号:WOS:000441871500063)】；

基金：This research was supported the Post Doctoral Fund of China (2015M571539), the Doctoral Program of Shan Dong Province (BS2013SF011), Scientific Research of Foundation of Shan Dong University (J14LI01), Scientific Research of Foundation of Weifang (2014GX027) and Shanghai Natural Science Foundation (17ZR1407800).

语种：英文

外文关键词：Matrix equation; Nonnegative definite solution; Positive definite solution; Rank; Inertia

摘要：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* = C and BXB* = 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 non-central Wishart random matrices is derived. Many results existing in the literature are extended. (C) 2018 Elsevier Inc. All rights reserved.