Abstract
In this paper necessary and sufficient conditions for the matrix equation to have a positive definite solution are derived, where , is an identity matrix, are nonsingular real matrices, and is an odd positive integer. These conditions are used to propose some properties on the matrices , . Moreover, relations between the solution and the matrices are derived.
Highlights
Consider the nonlinear matrix equation mX + ∑ ATi Xδi Ai = I, −1 < δi < 0, (1)i=1 where I is an real matrices, n × n identity matrix, Ai and m is an odd positive are n × integer n nonsingular (A∗i stands for the conjugate transpose of the matrix Ai)
I=1 where I is an real matrices, n × n identity matrix, Ai and m is an odd positive are n × integer n nonsingular (A∗i stands for the conjugate transpose of the matrix Ai)
We take X = WTW as a solution of the matrix equation (1)
Summary
I=1 where I is an real matrices, n × n identity matrix, Ai and m is an odd positive are n × integer n nonsingular (A∗i stands for the conjugate transpose of the matrix Ai). 13] have studied the existence, the rate of convergence, as well as the necessary and sufficient conditions of the existence of positive definite solutions of similar kinds of nonlinear matrix equations.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
