Necessary and Sufficient Conditions for the Existence of a Positive Definite Solution for the Matrix EquationX+∑i=1mAiTXδiAi=I

[摘要] In this paper necessary and sufficient conditions for the matrix equationX+∑i=1mAiTXδiAi=Ito have a positive definite solutionXare derived, where-1<δi<0,Iis ann×nidentity matrix,Aiaren×nnonsingular real matrices, andmis an odd positive integer. These conditions are used to propose some properties on the matricesAi,i=1,2,…,m. Moreover, relations between the solutionXand the matricesAiare derived.

[学科分类] 应用数学