Open AccessInequalities for the eigenvalues of the positive definite solutions of the nonlinear matrix equation
Author(s) -
Guoxing Wu,
Ting Xing,
Duo Zhou
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1909667w
Subject(s) - mathematics , hermitian matrix , positive definite matrix , eigenvalues and eigenvectors , matrix differential equation , matrix (chemical analysis) , mathematical analysis , pure mathematics , nonlinear system , differential equation , physics , quantum mechanics , materials science , composite material
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.