Inequalities for the eigenvalues of the positive definite solutions of the nonlinear matrix equation
Guoxing Wu, Ting Xing, Duanmei Zhou · Filomat · 2019
In this paper, the Hermitian positive definite solutions of the matrix equation Xs + A*X-tA = Q are considered, where Q is a Hermitian positive definite matrix, s and t are positive integers. Bounds for the sum of eigenvalues of the solutions to the equation are given. The equivalent conditions for solutions of the equation are obtained. The eigenvalues of the solutions of the equation with the case AQ = QA are investigated.